Information processing device, information processing method, and program

Abstract

To provide concrete investment strategy for improving a given evaluation index at the beginning of investment.SOLUTION: An information processing apparatus 1 includes a probability distribution calculation unit 51 which functions in a CPU 11 as follows, in calculating a probability distribution of a price of an asset at an end of a term, the asset being invested with predetermined investment strategy. The probability distribution calculation unit 51 is configured to: start investment by purchasing a first investment commodity using all investment money at the beginning when receiving an investment period, an investment amount at the beginning, N (N is an integer value of one or greater) switching amounts, an operation start time, and a parameter with which price fluctuation of N+1 investment commodities corresponding to the switching amount is assumed as geometric Brownian motion; and execute calculating a probability distribution of the investment price at the end of the term for the case of changing an investment target to a corresponding investment commodity every time each of the switching amounts is reached.SELECTED DRAWING: Figure 15

Description

[Technical Field]

[0001] The present invention relates to an information processing device, an information processing method, and a program relating to a method for optimizing an investment strategy that switches investment products during investment in a goal-based approach to asset management. [Background technology]

[0002] Generally, the asset management method known as the goal-based approach emphasizes clearly setting target amounts and investment periods in accordance with each individual's goals and needs. This approach enables efficient asset management by specifically defining investment objectives and customizing investment strategies based on those objectives. By setting appropriate target amounts and selecting investment periods, it is possible to secure the necessary funds and properly manage risk, thereby realizing asset management that meets an individual's long-term needs.

[0003] One example of a goal-based approach to asset management is the target-year fund. A target-year fund is a type of balanced investment trust that automatically adjusts its asset allocation to reduce the ratio of risky assets and shift to more stable management as it approaches a predetermined target year (the final target year for management).

[0004] Discretionary investment management, such as wrap accounts and robo-advisors, is important in the goal-based approach to asset management because it can provide investment strategies customized to each individual's risk tolerance. These investment services often use algorithms to recommend optimal asset allocations based on an individual's risk tolerance and set goals. This automated approach saves investors the trouble of having to create their own investment strategies, resulting in more efficient asset management.

[0005] In both mutual funds and discretionary investment, there are investment products or management services that automatically convert to cash or change to the lowest risk investment when a pre-set target amount is reached. Here, we will refer to this type of investment as profit-lock investment. Profit-lock investment is an important investment method in the goal-based approach, as it is investment that is carried out with the target amount in mind. [Prior art documents] [Non-patent literature]

[0006] [Non-Patent Document 1] TVERSKY, Amos; KAHNEMAN, Daniel. Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and uncertainty, 1992, 5: 297-323. [Non-patent document 2] DE GIORGI, Enrico; HENS, Thorsten. Making prospect theory fit for finance. Financial Markets and Portfolio Management, 2006, 20: 339-360. Summary of the Invention [Problem to be solved by the invention]

[0007] Each of the conventional operation services mentioned above has its own issues.

[0008] Target year funds automatically reduce the risk level when the remaining investment period reaches a predetermined period. This means that deviations from the target amount cannot be taken into account, and there is a problem that, for example, if the risk level is reduced even though the investment is far from the target amount, the deviation from the target amount may become large at the end of the investment period.

[0009] Because wrap accounts and robo-advisors manage investments according to a customer's risk tolerance, estimated in advance through assessments, few of them can automatically change the risk level based on certain conditions during the investment period. Even those that do have an automatic risk level change function often do so in response to market events, and do not take into account an individual's target amount or investment period.

[0010] Profit lock investments take into account the target amount in that the investment can be switched once the target amount is reached, but the initial risk level is always maintained until then, which means that the investment will continue to take high risks for a long period of time. For example, even if the asset price approaches the target amount, the risk level cannot be reduced, so there is a possibility of a large drop even near the target amount. [Means for solving the problem]

[0011] Similar to profit-lock investment, this invention is based on the idea of switching the risk level of an investment product when a certain amount is reached, but by expanding the amount at which the risk level is switched from one to multiple amounts, a more detailed investment strategy can be realized.

[0012] It also provides a means for determining the optimal parameters (some or all of the investment period and switching amount) through optimization calculations when an index that specifically evaluates the probability distribution of asset prices at the end of the period is given.

[0013] That is, the information processing device of the first aspect of the present invention is An information processing device that calculates a probability distribution of asset prices at the end of a period when investment is made according to a given investment strategy, a probability distribution calculation means for calculating a probability distribution of asset prices at the end of a period when, given an investment period, an investment amount at the beginning of the period, N (N is an integer value of 1 or more) switching amounts, and parameters when price fluctuations of N+1 investment products corresponding to the start of the period and the switching amounts are regarded as geometric Brownian motion, the investment is started by purchasing an initial investment product using the entire investment amount at the beginning of the period, and the investment target is changed to the corresponding investment product each time the respective switching amounts are first reached; Equipped with.

[0014] The information processing method and the program according to the first aspect of the present invention are respectively a method and a program corresponding to the information processing device according to the first aspect of the present invention.

[0015] The information processing device of the second aspect of the present invention comprises: An information processing device that calculates a probability distribution of asset prices at the end of a period when investment is made according to a given investment strategy, a probability distribution calculation means for calculating a probability distribution of an asset price at the end of a period when, given an investment period, a target amount, an investment amount at the beginning of the period, and a function returning an index of an investment product whose value is in the closed interval [0,1] from the amount (continuous value) from the investment amount at the beginning of the period to the target amount and a set of parameters when the price fluctuations of consecutive investment products indexed in the closed interval [0,1] are regarded as geometric Brownian motion, or a function returning an index of an investment product whose value is in the half-open interval [0,∞) from an amount (continuous value) equal to or greater than the investment amount at the beginning of the period and a set of parameters when the price fluctuations of consecutive investment products indexed in the half-open interval [0,∞) are regarded as geometric Brownian motion, the means starts investment by purchasing an initial investment product using the entire investment amount at the beginning of the period, and switches the investment target to the corresponding investment product each time the respective switching amounts are first reached; Equipped with.

[0016] An information processing method and a program according to a second aspect of the present invention are a method and a program corresponding to the information processing device according to the second aspect of the present invention.

[0017] An information processing device according to a third aspect of the present invention includes: An information processing device that optimizes parameters of an investment strategy to maximize or minimize a given evaluation index, a parameter optimization means for optimizing parameters of an investment strategy that maximizes or minimizes an evaluation index in a case where, when a quantitative evaluation index, an investment period, an investment amount at the beginning of the period, N (N is an integer value of 1 or more) switching amounts, and parameters when price fluctuations of N+1 investment products corresponding to the start of the operation and the switching amounts are regarded as geometric Brownian motion, the investment is started by purchasing an initial investment product using the entire investment amount at the beginning of the period, and the investment target is changed to the corresponding investment product each time each switching amount is first reached; Equipped with.

[0018] An information processing method and a program according to the third aspect of the present invention are a method and a program corresponding to the information processing device according to the third aspect of the present invention.

[0019] An information processing device according to a fourth aspect of the present invention includes: An information processing device that optimizes parameters of an investment strategy to maximize or minimize a given evaluation index, a parameter optimization means for optimizing parameters of an investment strategy that maximizes or minimizes an evaluation index when a quantitative evaluation index, an investment period, a target amount, an investment amount at the beginning of the period, a function that returns an index of an investment product that takes a value in a closed interval [0, 1] from the amount (continuous value) from the investment amount at the beginning of the period to the target amount, and a set of parameters when price fluctuations of consecutive investment products indexed in the closed interval [0, 1] are regarded as geometric Brownian motion, or a function that returns an index of an investment product that takes a value in a half-open interval [0, ∞) from an amount (continuous value) equal to or greater than the investment amount at the beginning of the period, and a set of parameters when price fluctuations of consecutive investment products indexed in the half-open interval [0, ∞) are regarded as geometric Brownian motion; Equipped with.

[0020] An information processing method and a program according to a fourth aspect of the present invention are a method and a program corresponding to the information processing device according to the fourth aspect of the present invention. [Effects of the Invention]

[0021] The present invention is an investment strategy proposed to solve the above-mentioned conventional problems, and can specifically provide an investment strategy that improves a given evaluation index at the beginning of the investment period. [Brief explanation of the drawings]

[0022] [Figure 1] FIG. 10 is a diagram showing the flow of operations using profit lock type operations. [Figure 2] FIG. 10 is a diagram showing the flow of operation using two-point switching operation. [Figure 3] FIG. 10 is a diagram showing the flow of operation in N-point switching operation. [Figure 4] This figure compares the probability density function obtained by Monte Carlo simulation and calculation for N-point switching operation. [Figure 5]This is a diagram showing the calculation flow of the probability density function of the end-of-period asset price probability distribution in N-point switching type management. [Figure 6] This graph compares the calculation speed when an investment product meets certain conditions and when those conditions are not used. [Figure 7] FIG. 10 is a diagram showing the flow of operation in continuous switching type operation. [Figure 8] FIG. 10 is a diagram showing the flow of calculation of the probability density function of the end-of-period asset price probability distribution in continuous switching type management. [Figure 9] FIG. 10 is a diagram comparing the probability density functions obtained by Monte Carlo simulation and calculation for continuous switching operation. [Figure 10] FIG. 10 is a diagram showing the calculation flow for optimizing parameters for N-point switching operation. [Figure 11] FIG. 10 is a diagram showing the transition of evaluation indexes due to parameter optimization of N-point switching type operation. [Figure 12] This figure shows the switching amount obtained by optimizing the 20-point switching operation. [Figure 13] FIG. 10 is a diagram showing a calculation flow for optimizing parameters for continuous switching operation. [Figure 14] 1 is a block diagram showing an example of a hardware configuration of an information processing apparatus to which the present invention is applied; [Figure 15] 15 is a functional block diagram showing an example of the functional configuration of the information processing device of FIG. 14. DETAILED DESCRIPTION OF THE INVENTION

[0023] Hereinafter, the calculation method and optimization method according to the present invention will be described with reference to the drawings.

[0024] <Probability distribution of profit-lock investment> First, let us consider the probability distribution of asset prices at the end of the period when investment is made using a profit-lock investment method. Hereafter, the probability distribution of asset prices at the end of the period will be referred to as the end-of-period asset price probability distribution. The investment amount at the beginning of the period will be referred to as the beginning investment amount hereafter. Figure 1 is a flowchart showing the operation flow of profit-lock investment. First, at the start of the operation, investment product 0 is purchased with the initial investment amount. After that, the investment is operated for a certain period (S1), and the investment period is checked to see if it has ended (S2). If it has not ended, the investment is checked to see if the target amount has been reached (S3). If it has not been reached, the investment is operated for another certain period (S1) and the confirmation of reaching the target amount is repeated. If it has been reached, reallocation is carried out from investment product 0 held to investment product 1 (S4), and the investment is operated for a certain period (S5), and the investment period is checked to see if it has ended (S6). The operation continues in this manner. Reallocation can be done by selling all of investment product 0 and purchasing investment product 1, or, if the investment product is a portfolio consisting of multiple financial products, by buying and selling the difference.

[0025] Let's consider calculating the end-of-period asset price probability distribution for profit-lock investment. In the following, we will assume that the target amount is confirmed at any time and do not take into account the gap of a certain period. This is thought to be a reasonable approximation if the investment period is sufficiently long compared to the certain period.

[0026] Assume that the asset price S of each investment product follows the geometric Brownian motion expressed by the following equation.

number

[0027] As parameters for profit lock management, the initial investment amount is set to 1, and the target amount is set to S G The operation period is t G Let the drift of investment product 0 be μ0 and its volatility be σ0, and the drift of investment product 1 be μ1 and its volatility be σ1.

[0028] If the initial investment amount is different from 1, then S Init When the initial investment amount is 1 and the target amount is S G / S Init The other variables are the same. If we set the random variable of the end-of-period asset valuation in the new profit-lock type investment as X, the random variable of the end-of-period asset valuation in the original investment is S Init X, so there is no lack of generality even if we only discuss the case where the initial investment amount is 1.

[0029] The probability density function of the end-of-period asset price probability distribution for profit-lock investment is calculated separately for the cases where the target amount is not reached during the period and for the cases where it is not reached during the period.

[0030] The contribution to the probability density function of not reaching the target amount can be calculated using the following formula:

number

[0031] where f LN is the probability density function of the log-normal distribution and is expressed by the following equation:

number

[0032] The contribution to the probability density function when the target amount is reached can be calculated using the following formula:

number

[0033] where f IG is the probability density function of the inverse Gaussian distribution and is expressed by the following equation:

number

[0034] Combining equations (2) and (4), the probability density function p(S) of the end-of-period asset price probability distribution for profit-lock investment can be calculated as follows:

number

[0035] <Probability distribution of two-point switching operation> Next, consider an investment strategy in which two amounts are set for switching between investment products. From now on, we will refer to this type of investment strategy as two-point switching type, and the amount for switching between investment products as the switching amount. Two-point switching type investment strategy can also be thought of as an extension of profit-lock type investment strategy, in which the larger switching amount is set as the target amount, and the investment product is switched to a third investment product at an amount lower than the target amount. Figure 2 is a flowchart showing the operation flow of the two-point switching investment model. First, at the start of the investment, investment product 0 is purchased with the initial investment amount. After that, the investment is carried out for a certain period (S11), and the investment period is checked to see if it has ended (S12). If it has not ended, the investment is checked to see if the switching amount has been reached (S13). If it has not, the investment is carried out for another certain period (S11) and the confirmation is repeated. If it has, reallocation is carried out from investment product 0 to investment product 1 (S14). After that, the investment is carried out for a certain period (S15), and the investment period is checked to see if it has ended (S16). If it has not ended, the investment is checked to see if it has reached the target amount (S17). If it has not, the investment is carried out for a certain period (S15) and the confirmation is repeated. If it has reached the target amount, reallocation is carried out from investment product 1 to investment product 2 (S18), and the investment is carried out for a certain period (S19), and the investment period is checked to see if it has ended (S20). This process continues.

[0036] Let's consider calculating the end-of-period asset price probability distribution for two-point switching investment. As with profit-lock investment, confirmation of whether the switching amount has been reached is done at any time, and we do not take into account the gaps in a certain period of time.

[0037] As parameters for two-point switching operation, the initial investment amount is 1, the first switching amount is S1, the second switching amount is S2, and the operation period is t G Let the drift of investment product 0 be μ0 and its volatility be σ0, the drift of investment product 1 be μ1 and its volatility be σ1, and the drift of investment product 2 be μ2 and its volatility be σ2.

[0038] The probability density function of the end-of-period asset price probability distribution for two-point switching management is calculated separately for the cases where the first switching amount is not reached during the period and for the cases where it is not reached during the period.

[0039] The contribution to the probability density function when the first switching amount is not reached can be calculated as follows, similar to equation (2).

number

[0040] In profit-lock investment, the initial investment amount is 1, the target amount is S2 / S1, the investment period is t, the drift of investment product 0 is μ1, the volatility is σ1, the drift of investment product 1 is μ2, the volatility is σ2. The probability density function of the asset price probability distribution at the end of the period is p PL Let (S; t). The contribution to the probability density function when the first switching amount is reached is the probability density function of the time until it is reached and the probability density function p of the end-of-period asset price probability distribution of the profit-lock type investment. PL It can be calculated using the convolution of (S; t) as follows:

number

[0041] Combining equations (7) and (8), the probability density function p(S) of the end-of-period asset price probability distribution for two-point switching management can be calculated as follows:

number

[0042] <Probability Distribution of N - point Switching Type Application (in the case of recursive calculation)> Consider an application with N switching amounts according to the same concept. Hereafter, this application will be referred to as the N - point switching type application. Figure 3 is a flowchart showing the operation flow of the N - point switching type application. First, at the start of the operation, investment product 0 is purchased with the initial investment amount, and 0 is assigned to the variable K indicating the number of the next switching amount (S31). Then, the operation is carried out for a certain period (S32), it is confirmed whether the operation period has ended (S33). If not, it is confirmed whether the (K + 1)-th switching amount has been reached (S34). If not, the operation for a certain period (S32) is carried out again and the confirmation of reaching is repeated. If it has been reached, reallocation from the held investment product K to investment product K + 1 is implemented (S35), and the value of K + 1 is assigned to K (S36). It is confirmed whether K is N (S37). If not, the operation for a certain period (S32) is carried out again and the confirmation of reaching is repeated. If K is N, the operation is carried out for a certain period (S38) and the confirmation of whether the operation period has ended (S39) is repeated to continue the operation.

[0043] Consider calculating the end - of - period asset price probability distribution of the N - point switching type application. Similar to before, the confirmation of reaching the switching amount is carried out at any time, and the consideration of a certain period opening is not taken into account.

[0044] As parameters in the N - point switching type application, the initial investment amount is set to 1, the K - th switching amount is S K and the operation period is t G and the drift of investment product K is μ K , the volatility is σ K and there are a total of N + 1 investment products, including those at the start of the operation and those corresponding to the N switching amounts.

[0045] Similar to the case of the 2 - point switching type application, the probability density function of the end - of - period asset price probability distribution of the N - point switching type application is calculated by dividing it into the case where the first switching amount is not reached during the period.

[0046] The contribution to the probability density function when the first switching amount is not reached can be calculated as follows, similar to equation (7).

number

[0047] In N-1 switching type management, the initial investment amount is 1, and the Kth switching amount is S K+1 / S1, the investment period is t, and the drift of investment product K is μ K+1 , volatility is σ K+1 The probability density function of the end-of-period asset price probability distribution is p N-1 Let (S;t). The contribution to the probability density function when the first switching amount is reached is the probability density function of the time until the first switching amount is reached and the probability density function p of the end-of-period asset price probability distribution of the above N-1 switching type management. N-1 Using the convolution of (S;t), it can be calculated as follows: However, when N = 3, the probability density function of the end-of-period asset price probability distribution in the two-point switching type investment described above is used as p2(S;t).

number

[0048] Combining equations (10) and (11), the probability density function p(S) of the end-of-period asset price probability distribution for N-point switching management can be calculated as follows:

number

[0049] The above calculation method reveals the N-point switching strategy type of recursive structure and has computational advantages in terms of being able to reuse it when the probability density function of the terminal asset price probability distribution of the switching strategy type up to N-1 points has been calculated in advance. However, there are also computational difficulties in terms of the need to calculate a multiple integral with complex terms when attempting to directly calculate the probability density function of the terminal asset price probability distribution of the N-point switching strategy type.

[0050] <Probability Distribution of N-Point Switching Type Operation (in the case of cumulative calculation)> Consider a method for calculating the probability density function of the terminal asset price probability distribution of the N-point switching type operation in a way different from before. The subsequent calculation method is to first calculate the probability distribution of the arrival time at each switching amount, then calculate the convolution with the probability density function of the terminal asset price probability distribution due to subsequent price movements, and finally sum them all up.

[0051] First, consider a description method for parameters that specifies N switching amounts to simplify the calculation.

[0052] For the k-th switching amount and the (k + 1)-th switching amount, when they are the last switching amount S N set the parameter κ k+1 to satisfy the following relationship. Assume that k ranges from 0 to N-1, and S0 required when calculating κ1 is arbitrarily set to 1 for convenience. S k ≦ S k+1 ≦ S N From this, κ k takes values in the closed interval [0, 1].

Equation

[0053] When the switching amount S k is given in advance, the parameter κ k+1 can be calculated by the following formula.

Equation

[0054] κ k Using A k , B k is defined as follows:

number

number

number

[0055] Using the above parameters, the kth switching amount can be calculated as follows:

number

[0056] Consider a method for calculating the probability distribution of the time to reach the Nth switching amount using the switching amounts parameterized by the above method.

[0057] Probability distribution of the time to reach the first switching price p fht 1 Since (t) is the probability distribution of the arrival time of geometric Brownian motion, it can be calculated as follows using the inverse Gaussian distribution.

number

[0058] The time to reach the second switching amount is the sum of the time to reach the first switching amount and the time it takes to reach the second switching amount after reaching the first switching amount, so it can be calculated as follows using the convolution of the probability density function of the inverse Gaussian distribution.

number

[0059] The above formula cannot be calculated analytically, so when actually performing numerical calculations, the G The calculation is performed by dividing the interval up to evenly and integrating the above formula at each point to find the value and approximating it with a piecewise linear function that is linearly interpolated. k If is small, f IG Since it approaches a delta function and cannot be well approximated, we set an appropriate threshold and A k If is less than that, the f IG can be calculated by regarding it as a delta function. In this case, p fht k (t) = p fht k-1 (t).

[0060] By repeating the same idea, the k+1th probability distribution can be calculated using the kth probability distribution as follows:

number

[0061] Using the probability distribution of the time when the Nth switching amount is reached, the probability density function of the end-of-period asset price probability distribution in N-point switching management is If the first switching amount is not reached When the kth switching amount is reached but the k+1th switching amount is not reached When the final switching amount is reached The calculation can be broadly divided into three cases.

[0062] First, the contribution to the probability density function when the first switching amount is not reached can be calculated using the following formula, similar to formula (10).

number

[0063] The contribution to the probability density function when the kth switching amount is reached but the k+1th switching amount is not reached can be calculated using the following formula.

number

[0064] The contribution to the probability density function when the final switching amount is reached can be calculated by the following formula:

number

[0065] Combining equations (22), (23), and (24), the probability density function of the end-of-period asset price probability distribution in N-point switching management can be calculated using the following equation.

number

[0066] In this example, the probability density function obtained by Monte Carlo simulation in five-point switching type management and the probability density function of the end-of-period asset price probability distribution according to equation (25) are calculated and compared. The parameters of five-point switching type management are the initial investment amount of 1, the switching amount, The first switching amount is 1.2, The second switching amount is 1.4, The third switching amount is 1.6, The fourth switching amount is 1.8, The fifth switching amount is 2.0, The investment period is 10 years, and each investment product is: The drift of investment product 0 is 0.797% (monthly rate), and the volatility is 2.887% (monthly rate). The drift of investment product 1 is 0.664% (monthly rate), and the volatility is 2.425% (monthly rate). The drift of investment product 2 is 0.533% (monthly rate), and the volatility is 1.963% (monthly rate). The drift of investment product 3 is 0.404% (monthly rate), and the volatility is 1.501% (monthly rate). The drift of investment product 4 is 0.277% (monthly rate), and the volatility is 1.039% (monthly rate). The drift of investment product 5 is 0.154% (monthly rate), the volatility is 0.577% (monthly rate), Let's say. In the Monte Carlo simulation, samples are generated according to the flowchart in Figure 3. We assume that the number of samples is 1 million, the fixed period of operation is one month, and the monthly returns follow a normal distribution with the drift of the investment product as the expected value and the volatility as the volatility. Figure 4 shows a line graph based on equation (25) and the results of the Monte Carlo simulation overlaid on a bar graph as a histogram with the number of bins set to 100. The calculation based on equation (25) is an approximation that does not take into account a fixed period of time, but it can be seen that the results are in good agreement with the results of the Monte Carlo simulation.

[0067] <Conditions for rigorously calculating the probability distribution of the time when the threshold is reached> In the above calculation method, the probability distribution of the time when the kth switching amount is reached is approximated by a piecewise linear function, so the accuracy of the calculation depends on the accuracy of the approximation. However, if the drift and volatility of the investment product satisfy a specific relationship, the reproducibility of the inverse Gaussian distribution makes it possible to perform an accurate calculation without using approximations. Below are three conditions that make this calculation possible.

[0068] First, the parameter A for the switching amount k and the drift and volatility of the investment product for any k

number

[0069] In this case, the probability density function of the time when the kth switching amount is reached can be calculated as follows:

number

[0070] Next, the drift and volatility of the investment product are

number

[0071] In this case, the probability density function of the probability distribution of the time when the kth switching amount is reached can be calculated as follows:

number

[0072] Finally, the drift and volatility of the investment product are given by a constant SR for any k.

number

[0073] At this time, the probability density function of the probability distribution of the time when the kth switching amount is reached can be calculated as follows:

number

[0074] Combining all of the above, the probability density function of the end-of-period asset price probability distribution for N-point switching investment can be calculated according to the flowchart shown in Figure 5. First, prepare the parameter values necessary for the calculation (S41). If the probability density function of the end-of-period asset price probability distribution for N-1-point switching investment required for the calculation has been determined (S42), calculate it using equation (12) (S43). If it has not been determined, check whether the investment product satisfies the conditions for rigorously calculating the probability distribution of the time at which the switching amount is reached (S44). If not, calculate the probability density function of the time at which each switching amount is reached using the approximation method described above (S45). If it is satisfied, calculate the probability density function of the time at which each switching amount is reached using the rigorous method of equation (27), equation (29), or equation (31) (S46). Then, the contribution when the switching amount is never reached (S47), the contribution when the kth switching amount is reached but the k+1th switching amount is not reached (S48), and the contribution when the final switching amount is reached (S49) are calculated, and by adding up each contribution (S50), the probability density function of the end-of-period asset price probability distribution for N-point switching type management can be calculated. [Example]

[0075] In this example, we compare the calculation speed between calculating the probability density function of the end-of-period asset price probability distribution for N-point switching type investment using an approximate method and calculating it exactly using equation (31) when the above-mentioned conditional equation (30) is satisfied. The parameters for N-point switching type investment are an initial investment amount of 1, an investment period of 10 years, the switching amount set by dividing the range from 1.0 to 2.0 into N equal parts, the volatility of the investment product divided into N equal parts from 0.577% (monthly rate) to 2.887% (monthly rate), and the drift calculated using equation (30) with an SR of 0.261, and the investment products are associated in descending order of volatility. Figure 6 compares the speed of calculations using approximate methods and exact calculations when the number of switching amounts is changed from 10 to 100. The calculation time for the exact 10-point switching strategy is set to 1, and the multiplication of the calculation time required for each case is plotted. We can see that the exact method is faster because it does not require approximation and does not require numerical integration. However, it is important to note that the exact calculation can only be used when the investment product meets the corresponding conditions.

[0076] <Probability distribution of continuous switching operation> As an extreme example of N-point switching type operation where N is very large, we can consider operation using continuous switching amounts. Hereafter, we will refer to this operation as continuous switching type operation. Continuous switching type operation can be divided into two types: when the range of switching amounts is bounded and when it is unbounded. The bounded case will be called bounded continuous switching type operation, and the unbounded case will be called unbounded continuous switching type operation. Figure 7 is a flowchart showing the operation flow of the continuous switching type investment. First, at the start of the operation, investment product 0 is purchased with the initial investment amount, and variable S high Initial investment amount S Init Then, the asset is managed for a certain period of time (S62), and it is confirmed whether the management period has ended (S63). If it has not ended, the asset valuation S at that time is S high If it is not high, the asset valuation amount is checked again by operating for a certain period (S62). If it is high, the asset valuation amount is checked again by operating for an unbounded continuous switching type (S65). If not, S is the target amount S. G If it is not higher, reallocate the investment product you are managing to the investment product corresponding to S (S67), and then S high (S68), and then operate for a certain period (S62) again to check the asset valuation amount repeatedly. If it is a bounded continuous switching type and S is S G If it is higher (S66), operation is performed for a certain period (S69), and the operation is continued by repeatedly checking whether the operation period has ended (S70).

[0077] Let us consider calculating the end-of-period asset price probability distribution for continuous switching investment. As before, confirmation of whether the switching amount has been reached is performed at any time, and we do not take into account the gaps in a certain period.

[0078] First, consider the bounded continuous switching type operation. As parameters in the bounded continuous switching type operation, the initial investment amount is set to 1, and the target amount is set to S G The operation period is t G Let z(S) be in the closed interval [1, S G Let μ(z) and σ(z) be functions that return the index of the investment product for each amount, from [μ(z)] to the closed interval [0, 1], and μ(z) and σ(z) be functions that return the drift and volatility of the corresponding investment product from the investment product index (closed interval [0, 1]). Investment products with continuous indexes can be realized by, for example, associating the index with the holding ratio when considering a two-asset portfolio of stocks and bonds.

[0079] The probability density function of the end-of-period asset price probability distribution for bounded continuous switching management is calculated separately for the cases where the target amount is reached and where it is not reached.

[0080] The contribution to the probability density function if the target amount is not reached can be calculated using the following formula:

number

[0081] Here, g(s, t) is a function that represents the probability density function of the time when the investment product first reaches the amount s as the investment product changes continuously, and can be calculated as follows.

number

[0082] The contribution to the probability density function when the target amount is reached can be written as follows:

number

[0083] Combining equations (32) and (34), the probability density function of the end-of-period asset price probability distribution for bounded continuous switching management can be calculated as follows:

number

[0084] Next, we consider unbounded continuous switching type investment. As parameters for unbounded continuous switching type investment, the initial investment amount is set to 1, and the investment period is set to t G Let z(S) be a function from the half-open interval [1, ∞) to the half-open interval [0, ∞) that returns the index of the investment product for each amount, and let μ(z) and σ(z) be functions that return the drift and volatility of the corresponding investment product from the investment product index (half-open interval [0, ∞)).

[0085] The probability density function of the end-of-period asset price probability distribution for unbounded continuous switching management can be calculated as follows:

number

[0086] Combining all of the above, the probability density function of the end-of-period asset price probability distribution for continuous switching investment can be calculated according to the flowchart shown in Figure 8. First, prepare the parameter values required for the calculation (S81), and calculate the probability density function of the arrival time to each asset price using equation (33) (S82). If the investment is not bounded continuous switching investment (S83), calculate the probability density function using equation (36) (S84). Otherwise, calculate the contribution if the target amount is not reached using equation (32) (S85) and the contribution if the target amount is reached using equation (34) (S86), and then add up each contribution (S87) to calculate the probability density function. [Example]

[0087] In this embodiment, in the bounded continuous switching operation, the probability density function obtained by Monte Carlo simulation and the probability density function of the terminal asset price probability distribution according to Equation (35) are calculated and compared. The parameters of the bounded continuous switching operation are such that the initial investment amount is 1, the target amount is 4, the operation period is 30 years, the function that returns the index of the investment product with the domain of [1, 4] is z(S) = (S - 1) / 3, the function that returns the drift of the investment product is μ(z) = 0.165% + z × 0.632%, and the function that returns the volatility is μ(z) = 0.577% + z × 2.309%. Samples for the Monte Carlo simulation are generated according to the flowchart of FIG. 7. The number of samples is 1 million, the operation for a certain period is 1 month, and it is assumed that the monthly return follows a normal distribution with the drift of the investment product as the expected value and the volatility as the volatility. FIG. 9 shows a graph in which the line graph according to Equation (35) and the results of the Monte Carlo simulation are shown as a bar graph in a histogram with 100 bins and overlapped. It can be confirmed that although the calculation according to Equation (25) is an approximation without considering a certain period, it is in good agreement with the results of the Monte Carlo simulation.

[0088] <Optimization Method for N-Point Switching Operation> Conventionally, the probability distribution of a complex operation strategy such as the N-point switching operation needs to be calculated using Monte Carlo simulation. The calculation efficiency is poor, and in addition to the calculation results being affected by noise, in order to obtain the optimal parameters under the given evaluation index, it is necessary to use inefficient methods such as grid search. However, based on the discussions so far, since the probability density function of the terminal asset price probability distribution of the N-point switching operation can be obtained analytically, when an index for quantitatively evaluating the terminal asset price probability distribution is given, its value can also be calculated analytically. As a result, it has become possible to execute the search for the optimal parameters using an optimization method.

[0089] An example of a quantitative evaluation index is the probability of achieving the target amount. G Using the probability density function p(S) of the end-of-period asset price probability distribution for N-point switching management, it can be calculated as follows:

number

[0090] Another example of a quantitative evaluation index is the evaluation method using prospect theory. The method of evaluating a continuous probability distribution using prospect theory is as follows.

[0091] X is a random variable representing the end-of-period asset price, F X Let X be the cumulative distribution function, and let S be the target amount. G , u + is the value function in the positive area from the reference point, u - is the value function in the negative area from the reference point, T + is the probability weighting function in the positive region from the reference point, T - Let be a probability weighting function in the negative region from the reference point, and assume that the reference point coincides with the target amount.

[0092] In this case, the evaluation index in prospect theory can be calculated using the following formula.

number

[0093] In prospect theory, the value function and probability weighting function are not fixed and their selection is arbitrary. In particular, when evaluating an object that takes unbounded, continuous values such as the probability distribution of asset prices, it has been pointed out in Non-Patent Document 2 that the commonly used value function, the piecewise power function proposed by Tversky and Kahneman in Non-Patent Document 1, causes the St. Petersburg Paradox. Therefore, when evaluating the end-of-period asset price probability distribution for N-point switching investment, calculations are performed using the piecewise exponential value function proposed by Giorgi and Hens in Non-Patent Document 2.

[0094] When calculating evaluation indicators in prospect theory, it is necessary to calculate the cumulative distribution function of the end-of-period asset price probability distribution for the N-point switching strategy. This is given by the following formula from the definition of the cumulative distribution function, and it can be calculated in three cases.

number

[0095] First, P1(X) can be calculated using the following formula:

number

[0096] Next is P2 k (X) can be calculated using the following formula:

number

[0097] Finally, P3(X) can be calculated using the following formula:

number

[0098] Combining equations (40), (41), and (42), the cumulative distribution function of the end-of-period asset price probability distribution for the N-point switching strategy can be calculated as follows:

number

[0099] To calculate the cumulative distribution function of the end-of-period asset price probability distribution for the above-mentioned N-point switching strategy type, it is necessary to calculate all contributions from switching amounts lower than the asset price argument, but when calculating a valuation index based on prospect theory by numerical integration, it is thought that the number of times the cumulative distribution function is evaluated at points higher than the switching amount will increase.Since the calculation of the complementary cumulative distribution function involves calculating only the contributions from switching amounts higher than the argument, it is thought that when calculating a valuation index based on prospect theory by numerical integration, it is more computationally efficient to use a form that uses the complementary cumulative distribution function.

[0100] When the complementary cumulative distribution function of X is written as , the following equation holds from the definition of the complementary cumulative distribution function.

number

[0101] Therefore, the evaluation index in prospect theory using the complementary cumulative distribution function can be calculated using the following formula:

number

[0102] The complementary cumulative distribution function of the end-of-period asset price probability distribution for the N-point switching strategy is defined as follows, and it can be seen that it can be calculated in three cases, just like the cumulative distribution function.

number

[0103] First, P1(X) with a macron can be calculated using the following formula (P with a macron means P with a bar above it, and the same applies below).

number

[0104] Next is P2 with Macron k (X) can be calculated using the following formula:

number

[0105] Finally, P3(X) with macrons can be calculated using the following formula:

number

[0106] To summarize the above, the complementary cumulative distribution function of the end-of-period asset price probability distribution for the N-point switching strategy can be calculated as follows:

number

[0107] The final example of a quantitative evaluation index is the mth moment around the target amount. G The mth moment around can be calculated by definition as follows:

number

[0108] The mth moment around the target amount can be calculated using the moments around the origin up to the mth order as follows:

number

[0109] The mth moment around the origin is defined as follows, and it can be calculated in three cases.

number

[0110] First, E1 m can be calculated by the following formula:

number

[0111] Here, F IG is the cumulative distribution function of the inverse Gaussian distribution, as expressed by the following equation:

number

[0112] Next, E2 m,k can be calculated by the following formula:

number

[0113] Finally, E3 m can be calculated by the following formula:

number

[0114] Combining equations (54), (56), and (57), the m-th moment around the origin can be calculated as follows:

number

[0115] As described above, if quantitative evaluation indicators are given, they can be calculated analytically, and the parameters of the investment strategy (some or all of the investment period and switching amount) that maximize or minimize the given evaluation indicators can be found using optimization techniques.

[0116] In particular, the formula for the end-of-period asset price probability distribution of the N-point switching strategy is differentiable with respect to the investment period and switching amount, so if the evaluation index is also differentiable, it can be optimized using optimization methods that use gradient information, such as gradient descent or the quasi-Newton method (BFGS). The derivatives with respect to each parameter can be found analytically, but they can also be calculated programmatically using automatic differentiation.

[0117] If it takes a long time to evaluate the derivative using the automatic differentiation described above, or if the evaluation index is not differentiable in the first place, it is possible to consider optimization methods that do not use gradient information, such as genetic algorithms or CMA-ES.

[0118] The optimization framework described above can be summarized in a flowchart, as shown in Figure 10, and calculations can be performed according to it. First, a quantitative evaluation index is given (S91). Next, parameters that are not to be optimized are given (S92), and initial values of parameters that are to be optimized are given (S93). If the evaluation index is differentiable (S94), optimization is performed using an optimization method that uses gradient information (S95). Conversely, if it is not differentiable or the cost of calculating the derivative is high, optimization is performed using an optimization method that does not require gradient information (S96). As a result of optimization, optimized parameters are obtained (S97). [Example]

[0119] In this example, the switching amount for N-point switching investment is actually optimized using the second-order moment around the target amount as an evaluation index. Since the smaller the value of the evaluation index, the closer the asset price at the end of the period is to the target amount, optimization is performed to reduce the evaluation index. The parameters for N-point switching investment are an initial investment amount of 1, a target amount of 2, and a 10-year investment period. The switching amount is fixed at the final switching amount, with the remaining values determined through optimization. The volatility of the investment products is divided into N equal parts from 0.866% (monthly rate) to 2.598% (monthly rate), and the drift is calculated using equation (30) with an SR of 0.280, with investment products being assigned in descending order of volatility. The initial switching amount is set by dividing the target amount from the initial investment amount into N equal parts. CMA-ES is used as the optimization method. Figure 11 shows the transition of the value of the evaluation index after optimization when N is changed from 2 to 20. It can be seen that the value of the evaluation index decreases as the switching amount increases. Figure 12 shows the switching amount values, which are the optimization results for the 20-point switching strategy. It can be seen that the risk level gradually decreases from around 1.5, just before the target amount.

[0120] <Optimization method for continuous switching operation> As with N-point switching management, it is now possible to analytically determine the probability density function of the end-of-period asset price probability distribution in continuous switching management, so when an index that quantitatively evaluates the end-of-period asset price probability distribution is given, its value can also be analytically calculated. As a result, it is now possible to use optimization methods to search for optimal parameters.

[0121] When optimizing the end-of-period asset price probability distribution for continuous switching investment, a parameterized function z(S) is used to return the index of the investment product. For example, by determining m characteristic functions in advance and expressing z(S) as a linear combination of them, it is possible to reduce the optimization to an m-dimensional vector.

number

[0122] The optimization framework described above can be summarized in a flowchart, as shown in Figure 13, and calculations can be performed according to it. First, a quantitative evaluation index is given (S101). Next, parameters that are not to be optimized are given (S102), and initial values of parameters to be optimized are given (S103). If the evaluation index is differentiable (S104), optimization is performed using an optimization method that uses gradient information (S105). Conversely, if it is not differentiable or the cost of calculating the derivative is high, optimization is performed using an optimization method that does not require gradient information (S106). As a result of optimization, optimized parameters are obtained (S107).

[0123] <Devices that realize optimization methods> FIG. 14 is a block diagram showing an example of the hardware configuration of an information processing device to which the present invention is applied. The optimization method for N-point switching type operation and the optimization method for continuous switching type operation can be executed using, for example, an information processing device 1 shown in Fig. 14. That is, the information processing device 1 shown in Fig. 14 is a device having the function of executing each step shown in Fig. 10 and Fig. 13.

[0124] The information processing device 1 includes a CPU (Central Processing Unit) 11, a ROM (Read Only Memory) 12, a RAM (Random Access Memory) 13, a bus 14, an input / output interface 15, an output unit 16, an input unit 17, a memory unit 18, a communication unit 19, and a drive 20.

[0125] The CPU 11 executes various processes according to a program recorded in the ROM 12 or a program loaded from the storage unit 18 into the RAM 13 . The RAM 13 also stores data and the like necessary for the CPU 11 to execute various processes.

[0126] The CPU 11, ROM 12, and RAM 13 are interconnected via a bus 14. An input / output interface 15 is also connected to this bus 14. An output unit 16, an input unit 17, a memory unit 18, a communication unit 19, and a drive 20 are connected to the input / output interface 15.

[0127] The output unit 16 is composed of various liquid crystal displays and the like, and outputs various information. The input unit 17 is made up of various hardware buttons and the like, and is used to input various information. The storage unit 18 is configured with a DRAM (Dynamic Random Access Memory) or the like, and stores various data. The communication unit 19 controls communications with other devices via a network including the Internet.

[0128] The drive 20 is provided as needed. Removable media 30, such as a magnetic disk, optical disk, magneto-optical disk, or semiconductor memory, is appropriately attached to the drive 20. Programs read from the removable media 30 by the drive 20 are installed in the storage unit 18 as needed. The removable media 30 can also store various data stored in the storage unit 18 in the same way as the storage unit 18.

[0129] [Functional configuration] Next, the functions of the information processing device 1 will be described with reference to FIG. FIG. 15 is a functional block diagram showing an example of the functional configuration of the information processing device 1 of FIG.

[0130] As shown in FIG. 15, in the CPU 11 of the information processing device 1, when the optimization method for N-point switching type operation and the optimization method for continuous switching type operation are executed, a probability distribution calculation unit 51 and a parameter optimization unit 52 function.

[0131] In the first mode in which the information processing device 1 calculates the probability distribution of asset prices at the end of a period when investment is made according to a given investment strategy, the probability distribution calculation unit 51 in the CPU 11 functions as follows. That is, when the probability distribution calculation unit 51 is given an investment period, an investment amount at the beginning of the period, N (N is an integer value greater than or equal to 1) switching amounts, and parameters when the price fluctuations of N+1 investment products corresponding to the start of the investment and the switching amounts are considered as geometric Brownian motion, the probability distribution calculation unit 51 calculates the probability distribution of the asset price at the end of the period when the investment period is started by purchasing the first investment product using the entire investment amount at the beginning of the period, and then changes the investment target to the corresponding investment product each time the respective switching amounts are first reached.

[0132] Here, the probability distribution calculation unit 51 can perform the calculations for cases where the parameters satisfy specific conditions when the price fluctuations of the investment product are regarded as the geometric Brownian motion. This allows the calculation to be performed more simply and quickly.

[0133] In the second mode in which the information processing device 1 calculates the probability distribution of asset prices at the end of a period when investment is made according to a given investment strategy, the probability distribution calculation unit 51 in the CPU 11 functions as follows. That is, when the probability distribution calculation unit 51 is given an investment period, a target amount, an investment amount at the beginning of the period, and a function that returns an index of an investment product that takes a value in the closed interval [0,1] from the amount (continuous value) from the investment amount at the beginning of the period to the target amount and a set of parameters when the price fluctuations of consecutive investment products indexed in the closed interval [0,1] are regarded as geometric Brownian motion, or a function that returns an index of an investment product that takes a value in the half-open interval [0,∞) from an amount (continuous value) equal to or greater than the investment amount at the beginning of the period and a set of parameters when the price fluctuations of consecutive investment products indexed in the half-open interval [0,∞) are regarded as geometric Brownian motion, the probability distribution calculation unit 51 calculates the probability distribution of the asset price at the end of the period for an investment in which the entire investment amount at the beginning of the period is used to purchase the first investment product and the investment target is changed to the corresponding investment product each time the respective switching amounts are first reached.

[0134] Furthermore, in the third mode in which the information processing device 1 optimizes the parameters of the management strategy so as to maximize or minimize a given evaluation index, the parameter optimization unit 52 in the CPU 11 functions as follows. That is, when a quantitative evaluation index, an investment period, an investment amount at the beginning of the period, N (N is an integer value of 1 or more) switching amounts, and parameters when the price fluctuations of N+1 investment products corresponding to the start of the period and the switching amounts are considered as geometric Brownian motion are given, the parameter optimization unit 52 optimizes the parameters of the investment strategy that maximizes or minimizes the evaluation index in the case where the investment is started by purchasing the first investment product using the entire investment amount at the beginning of the period, and the investment target is changed to the corresponding investment product each time the respective switching amounts are first reached.

[0135] Here, the parameter optimization unit 52 can optimize some or all of the investment period and the switching amount as the parameters of the investment strategy that maximizes or minimizes the evaluation index.

[0136] Furthermore, utility based on cumulative prospect theory can be used as an evaluation index. This makes it possible to reduce the amount of calculation and reduce numerical instability.

[0137] Furthermore, in the fourth mode in which the information processing device 1 optimizes the parameters of the management strategy to maximize or minimize a given evaluation index, the parameter optimization unit 52 in the CPU 11 functions as follows. That is, when a quantitative evaluation index, an investment period, a target amount, an investment amount at the beginning of the period, and a function that returns an index of an investment product that takes a value in the closed interval [0, 1] from the amount (continuous value) from the investment amount at the beginning of the period to the target amount and a set of parameters when the price fluctuations of consecutive investment products indexed in the closed interval [0, 1] are regarded as geometric Brownian motion, or a function that returns an index of an investment product that takes a value in the half-open interval [0, ∞) from an amount (continuous value) equal to or greater than the investment amount at the beginning of the period and a set of parameters when the price fluctuations of consecutive investment products indexed in the half-open interval [0, ∞) are regarded as geometric Brownian motion, the parameter optimization unit 52 optimizes the parameters of an investment strategy that maximizes or minimizes the evaluation index in a case where an investment is started by purchasing an initial investment product using the entire investment amount at the beginning of the period, and the investment target is changed to the corresponding investment product each time the respective switching amounts are first reached.

[0138] Here, the parameter optimization unit 52 can optimize some or all of the investment period and the switching amount as the parameters of the investment strategy that maximizes or minimizes the evaluation index.

[0139] In other words, the information processing device 1 also functions as an optimization device for an investment strategy that switches investment products during the asset management of the goal-based approach. That is, when a target amount, an investment period, and a group of investment products to be invested are given, the information processing device 1 sets multiple milestone amounts up to the target amount, and controls the probability distribution of the asset valuation at the end of the period by switching investment products when the target amount is reached during the investment period.Furthermore, when an index that quantitatively evaluates the probability distribution of the asset valuation is given, the information processing device 1 can quickly calculate the parameters to be optimized using an optimization method.

[0140] Although one embodiment of the present invention has been described above, the present invention is not limited to the above-described embodiment, and modifications, improvements, etc. within the scope of achieving the object of the present invention are included in the present invention.

[0141] For example, the hardware configuration shown in FIG. 14 is merely an example for achieving the object of the present invention, and is not particularly limited.

[0142] Furthermore, the functional block diagram shown in Fig. 15 is merely an example and is not particularly limited. That is, it is sufficient that the information processing system is provided with a function that can execute the above-described series of processes as a whole, and the type of functional block used to realize this function is not particularly limited to the example of Fig. 15.

[0143] Furthermore, the locations of the functional blocks are not limited to those shown in FIG. 15 and may be arbitrary. Furthermore, one functional block may be configured as a single piece of hardware, a single piece of software, or a combination thereof.

[0144] When the processing of each functional block is performed by software, the program that constitutes the software is installed into a computer or the like from a network or a recording medium. The computer may be a computer built into dedicated hardware, or may be a computer capable of executing various functions by installing various programs, such as a server, a general-purpose smartphone, or a personal computer.

[0145] The recording medium containing such a program may not only be composed of removable media that is distributed separately from the device itself in order to provide the program to each user, but may also be composed of recording media that are provided to each user in a state where they are pre-installed in the device itself.

[0146] In this specification, the steps describing the program to be recorded on the recording medium include not only processes that are performed in chronological order, but also processes that are not necessarily performed in chronological order but are performed in parallel or individually.

[0147] In addition, in this specification, the term "system" refers to an overall device that is made up of a plurality of devices, a plurality of means, and the like.

[0148] In summary, the information processing apparatus to which the present invention is applied is sufficient if it has the following configuration, and can take on a variety of different embodiments.

[0149] That is, the information processing device of the first aspect to which the present invention is applied (for example, the information processing device 1 of FIG. 13) is An information processing device that calculates a probability distribution of asset prices at the end of a period when investment is made according to a given investment strategy, a probability distribution calculation means (e.g., the probability distribution calculation unit 51 in FIG. 14 ) for calculating the probability distribution of asset prices at the end of a period when, given an investment period, an investment amount at the beginning of the period, N (N is an integer value equal to or greater than 1) switching amounts, and parameters when price fluctuations of N+1 investment products corresponding to the start of the period and the switching amounts are regarded as geometric Brownian motion, the investment is started by purchasing the first investment product using the entire investment amount at the beginning of the period, and the investment target is changed to the corresponding investment product each time the respective switching amounts are first reached; Equipped with.

[0150] the probability distribution calculation means executes the calculation for a case where the parameters satisfy specific conditions when the price fluctuation of the investment product is regarded as the geometric Brownian motion; It is possible. This allows the calculation to be performed more simply and quickly.

[0151] In addition, the information processing device of the second aspect to which the present invention is applied (for example, the information processing device 1 of FIG. 13) is An information processing device that calculates a probability distribution of asset prices at the end of a period when investment is made according to a given investment strategy, a probability distribution calculation unit (e.g., the probability distribution calculation unit 51 in FIG. 14 ) for calculating a probability distribution of an asset price at the end of a period when, given an investment period, a target amount, an investment amount at the beginning of the period, and a function that returns an index of an investment product that takes a value in a closed interval [0, 1] from the amount (continuous value) between the investment amount at the beginning of the period and the target amount, and a set of parameters when the price fluctuations of consecutive investment products indexed in the closed interval [0, 1] are regarded as geometric Brownian motion, or a function that returns an index of an investment product that takes a value in a half-open interval [0, ∞) from an amount (continuous value) equal to or greater than the investment amount at the beginning of the period, and a set of parameters when the price fluctuations of consecutive investment products indexed in the half-open interval [0, ∞) are regarded as geometric Brownian motion, the investment is started by purchasing an initial investment product using the entire investment amount at the beginning of the period, and the investment target is changed to the corresponding investment product each time the respective switching amounts are first reached; Equipped with.

[0152] Furthermore, an information processing device of a third aspect to which the present invention is applied (for example, the information processing device 1 of FIG. 13) is An information processing device that optimizes parameters of an investment strategy to maximize or minimize a given evaluation index, a parameter optimization means (for example, the parameter optimization unit 52 in FIG. 14 ) for optimizing parameters of an investment strategy that maximizes or minimizes an evaluation index in a case where, when a quantitative evaluation index, an investment period, an investment amount at the beginning of the period, N (N is an integer value of 1 or more) switching amounts, and parameters when price fluctuations of N+1 investment products corresponding to the start of the investment and the switching amounts are considered as geometric Brownian motion, the investment is started by purchasing an initial investment product using the entire investment amount at the beginning of the period, and the investment target is changed to the corresponding investment product each time the respective switching amounts are first reached; Equipped with.

[0153] The parameter optimization means optimizes a part or all of the investment period and the switching amount as the parameters of the investment strategy that maximizes or minimizes the evaluation index. It is possible.

[0154] The evaluation index uses utility based on cumulative prospect theory. It is possible. This makes it possible to reduce the amount of calculation and reduce numerical instability.

[0155] Further, an information processing device of a fourth aspect to which the present invention is applied (for example, the information processing device 1 of FIG. 13) is An information processing device that optimizes parameters of an investment strategy to maximize or minimize a given evaluation index, a parameter optimization means (e.g., the parameter optimization unit 52 of FIG. 14 ) for optimizing parameters of an investment strategy that maximizes or minimizes an evaluation index when a quantitative evaluation index, an investment period, a target amount, an investment amount at the beginning of the period, a function that returns an index of an investment product that takes a value in a closed interval [0, 1] from the amount (continuous value) from the investment amount at the beginning of the period to the target amount, and a set of parameters when price fluctuations of consecutive investment products indexed in the closed interval [0, 1] are regarded as geometric Brownian motion, or a function that returns an index of an investment product that takes a value in a half-open interval [0, ∞) from an amount (continuous value) equal to or greater than the investment amount at the beginning of the period, and a set of parameters when price fluctuations of consecutive investment products indexed in the half-open interval [0, ∞) are regarded as geometric Brownian motion; Equipped with.

[0156] The parameter optimization means optimizes a part or all of the investment period and the switching amount as the parameters of the investment strategy that maximizes or minimizes the evaluation index. It is possible. [Explanation of symbols]

[0157] 1. Information processing device, 11: CPU, 12: ROM, 13: RAM, 14: bus, 15: input / output interface, 16: output unit, 17: input unit, 18: storage unit, 19: communication unit, 20: drive, 30: removable media, 51. Probability distribution calculation unit, 52. Parameter optimization unit

Claims

1. An information processing device that calculates a probability distribution of asset prices at the end of a period when investment is made according to a given investment strategy, a probability distribution calculation means for calculating a probability distribution of asset prices at the end of a period when, given an investment period, an investment amount at the beginning of the period, N (N is an integer value of 1 or more) switching amounts, and parameters when price fluctuations of N+1 investment products corresponding to the start of the period and the switching amounts are regarded as geometric Brownian motion, the investment is started by purchasing an initial investment product using the entire investment amount at the beginning of the period, and the investment target is changed to the corresponding investment product each time the respective switching amounts are first reached, The probability distribution calculation means Calculating a probability density function of the probability distribution of the asset price at the end of the period separately into a contribution when the switching amount is never reached and a contribution when each switching amount is reached; Calculating the contribution to the probability density function of the case where the switching amount has never been reached using a log-normal probability density function; Calculating the contribution to the probability density function when the switching amount is reached by convolving the probability density function of the time until the switching amount is reached with the probability density function of the end-of-period asset price probability distribution of the investment product after the switching amount is reached; summing the contributions to calculate a probability distribution of the asset price at the end of the period; Information processing device.

2. the probability distribution calculation means executes the calculation for a case where the parameters satisfy specific conditions when the price fluctuation of the investment product is regarded as the geometric Brownian motion, thereby omitting the convolution calculation and calculating the probability distribution in a closed form; The information processing device according to claim 1 .

3. An information processing method for calculating a probability distribution of asset prices at the end of a period when investment is made according to a given investment strategy, comprising: The method includes a probability distribution calculation step of calculating a probability distribution of asset prices at the end of a period when, given an investment period, an investment amount at the beginning of the period, N (N is an integer value of 1 or more) switching amounts, and parameters when price fluctuations of N+1 investment products corresponding to the start of the period and the switching amounts are regarded as geometric Brownian motion, the method starts by purchasing an initial investment product using the entire investment amount at the beginning of the period, and changes the investment target to the corresponding investment product each time the respective switching amounts are first reached, The probability distribution calculation step includes: calculating a probability density function of the probability distribution of the asset price at the end of the period by dividing it into a contribution when the switching amount is never reached and a contribution when each switching amount is reached; calculating a contribution to the probability density function in the case where the switching amount has never been reached using a log-normal probability density function; a step of calculating the contribution to the probability density function when the switching amount is reached by convolving the probability density function of the time until the switching amount is reached with the probability density function of the end-of-period asset price probability distribution of the investment product after the switching amount is reached; summing the contributions to calculate a probability distribution of the asset price at the end of the period; An information processing method including:

4. A computer that calculates the probability distribution of asset prices at the end of a period when a given investment strategy is implemented is When an investment period, an investment amount at the beginning of the period, N (N is an integer value of 1 or more) switching amounts, and parameters when price fluctuations of N+1 investment products corresponding to the start of the investment and the switching amounts are regarded as geometric Brownian motion are given, a control process is executed including a probability distribution calculation step for calculating a probability distribution of asset prices at the end of the period in the case where an investment is started by purchasing an initial investment product using the entire investment amount at the beginning of the period, and an investment is made by changing the investment target to the corresponding investment product each time the respective switching amounts are first reached, The probability distribution calculation step includes: calculating a probability density function of the probability distribution of the asset price at the end of the period by dividing it into a contribution when the switching amount is never reached and a contribution when each switching amount is reached; calculating a contribution to the probability density function in the case where the switching amount has never been reached using a log-normal probability density function; a step of calculating the contribution to the probability density function when the switching amount is reached by convolving the probability density function of the time until the switching amount is reached with the probability density function of the end-of-period asset price probability distribution of the investment product after the switching amount is reached; summing the contributions to calculate a probability distribution of the asset price at the end of the period; A program that executes control processing including:

5. An information processing device that calculates a probability distribution of asset prices at the end of a period when investment is made according to a given investment strategy, the system includes a probability distribution calculation means for calculating a probability distribution of asset prices at the end of a period when, given an investment period, a target amount, an investment amount at the beginning of the period, a function that returns an index of an investment product that takes a value in a closed interval [0, 1] from the amount (continuous value) from the investment amount at the beginning of the period to the target amount, and a set of parameters when price fluctuations of consecutive investment products indexed in the closed interval [0, 1] are regarded as geometric Brownian motion, or a function that returns an index of an investment product that takes a value in a half-open interval [0, ∞) from an amount (continuous value) equal to or greater than the investment amount at the beginning of the period, and a set of parameters when price fluctuations of consecutive investment products indexed in the half-open interval [0, ∞) are regarded as geometric Brownian motion, the system starts investment by purchasing an initial investment product using the entire investment amount at the beginning of the period, and changes the investment target to the corresponding investment product each time the respective switching amounts are first reached, The probability distribution calculation means Calculating the probability density function of the probability distribution of the asset price at the end of the period separately into contributions in the case where the target amount is not reached and contributions in the case where the target amount is reached; Calculating the contribution to the probability density function in the case where the target amount is not reached using the probability density function of the time when a specific asset price is first reached during the period and the index of the investment product corresponding to the asset price; Calculating the contribution to the probability density function when the target amount is reached using the probability density function of the time when the target amount is reached and the probability density function of a log-normal distribution; summing the contributions to calculate a probability distribution of the asset price at the end of the period; Information processing device.

6. An information processing method executed by an information processing device for calculating a probability distribution of asset prices at the end of a period when investment is made according to a given investment strategy, comprising: the method includes a probability distribution calculation step of calculating a probability distribution of asset prices at the end of a period when, given an investment period, a target amount, an investment amount at the beginning of the period, a function that returns an index of an investment product that takes a value in the closed interval [0, 1] from the amount (continuous value) from the investment amount at the beginning of the period to the target amount, and a set of parameters when the price fluctuations of consecutive investment products indexed in the closed interval [0, 1] are regarded as geometric Brownian motion, or a function that returns an index of an investment product that takes a value in the half-open interval [0, ∞) from an amount (continuous value) equal to or greater than the investment amount at the beginning of the period, and a set of parameters when the price fluctuations of consecutive investment products indexed in the half-open interval [0, ∞) are regarded as geometric Brownian motion, the method includes a probability distribution calculation step of calculating a probability distribution of asset prices at the end of the period when the investment amount at the beginning of the period is used to purchase an initial investment product and the investment target is changed to the corresponding investment product each time the respective switching amounts are first reached, The probability distribution calculation step includes: calculating a probability density function of the probability distribution of the asset price at the end of the period, dividing it into a contribution when the target amount is not reached and a contribution when the target amount is reached; a step of calculating a contribution to a probability density function in the case where the target amount is not reached, using a probability density function of a time when a specific asset price is reached for the first time during a period and an index of an investment product corresponding to the asset price; calculating a contribution to a probability density function when the target amount is reached using a probability density function of the time when the target amount is reached and a probability density function of a log-normal distribution; summing the contributions to calculate a probability distribution of the asset price at the end of the period; An information processing method including:

7. A computer that calculates the probability distribution of asset prices at the end of a period when a given investment strategy is implemented is execute a control process including a probability distribution calculation step for calculating a probability distribution of asset prices at the end of a period when, given an investment period, a target amount, an investment amount at the beginning of the period, a function that returns an index of an investment product that takes a value in the closed interval [0, 1] from the amount (continuous value) between the investment amount at the beginning of the period and the target amount, and a set of parameters when the price fluctuations of consecutive investment products indexed in the closed interval [0, 1] are regarded as geometric Brownian motion, or a function that returns an index of an investment product that takes a value in the half-open interval [0, ∞) from an amount (continuous value) equal to or greater than the investment amount at the beginning of the period, and a set of parameters when the price fluctuations of consecutive investment products indexed in the half-open interval [0, ∞) are regarded as geometric Brownian motion, the control process including a probability distribution calculation step for calculating a probability distribution of asset prices at the end of the period when the investment amount at the beginning of the period is used to purchase an initial investment product and the investment target is changed to the corresponding investment product each time the respective switching amounts are first reached, The probability distribution calculation step includes: calculating a probability density function of the probability distribution of the asset price at the end of the period, dividing it into a contribution when the target amount is not reached and a contribution when the target amount is reached; a step of calculating a contribution to a probability density function in the case where the target amount is not reached, using a probability density function of a time when a specific asset price is reached for the first time during a period and an index of an investment product corresponding to the asset price; calculating a contribution to a probability density function when the target amount is reached using a probability density function of the time when the target amount is reached and a probability density function of a log-normal distribution; summing the contributions to calculate a probability distribution of the asset price at the end of the period; A program that executes control processing including:

Images