Information processing apparatus, 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 a method for optimizing an operation strategy for switching investment products during operation in asset management using a goal-based approach, an information processing apparatus, an information processing method, and a program.

Background Art

[0002] Generally, an asset management method known as a goal-based approach emphasizes clearly setting a target amount and an operation period according to an individual's goals and needs. This approach enables efficient asset management by specifically defining the purpose of investment and customizing the operation strategy based on it. By setting an appropriate target amount and selecting an appropriate operation period, necessary funds can be secured and risks can be appropriately managed, so that asset management that meets an individual's long-term needs can be realized.

[0003] One representative example of asset management using a goal-based approach is a target-date fund. A target-date fund is a type of balanced investment trust that automatically changes the asset allocation to lower the risk asset ratio as it approaches a predetermined target year (the final target year of operation) and shifts to a stable operation.

[0004] Discretionary investment operations such as wrap accounts and robo-advisors are important in asset management using a goal-based approach in that they can provide an investment strategy customized according to an individual's risk tolerance. These operation services can often propose an optimal asset allocation based on an algorithm from an individual's risk tolerance and set goals. This automated approach saves the investor the trouble of formulating an operation strategy by themselves and realizes efficient asset management.

[0005] There exists an investment product or operation service that, in either an investment trust or discretionary investment, automatically cashes out once a preset target amount is reached, or changes to the least risky operation. Here, such an operation will be referred to as a profit lock - type operation. From the perspective of conducting operations with the target amount in mind, the profit lock - type operation is one of the important operation methods in the goal - based approach.

Prior Art Documents

Non - Patent Documents

[0006]

Non - Patent Document 1

Non - Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0007] The above - mentioned conventional operation services each have problems.

[0008] The target - year fund automatically reduces the risk level when the remaining operation period reaches a preset period. Therefore, it cannot consider the deviation from the target amount. For example, even though it is far from the target amount, if the risk level is reduced as a result, there is a problem that the deviation from the target amount may become large at the end of the operation period.

[0009] Since wrap accounts and robo-advisors operate in accordance with the risk tolerance of customers estimated in advance through assessment or the like, there are few that can automatically switch the risk level based on certain conditions during the operation period. Even those in which automatic switching of the risk level is implemented are mostly adjusted according to market events and do not take into account the individual's target amount or investment period.

[0010] Profit lock-type operation can consider the target amount from the perspective that the operation can be switched when the target amount is reached. However, since the initial risk level is always maintained until then, there is a problem that high risks are continuously taken for a long time. For example, even if the asset price approaches the target amount, the risk level cannot be lowered, so there is a possibility of a large decline even near the target amount.

Means for Solving the Problem

[0011] In the present invention, similar to the profit lock-type operation, based on the concept of switching the risk level of investment products when a certain amount is reached, a more detailed operation strategy is realized by expanding the amount at which the risk level is switched from one to a plurality.

[0012] In addition, when an index for specifically evaluating the probability distribution of the asset price at the end of the period is given, means for obtaining the optimal parameters (part or all of the investment period and the switching amount) by optimization calculation are also provided.

[0013] That is, the information processing apparatus according to the first aspect of the present invention is an information processing apparatus that calculates the probability distribution of the asset price at the end of the period when operating according to a given operation strategy. When an operation period, an investment amount at the beginning, N switching amounts (where N is an integer value of 1 or more), and parameters when the price fluctuations of N + 1 investment products corresponding to the start of operation and the switching amounts are regarded as geometric Brownian motion are given, the probability distribution calculation means for calculating the probability distribution of the asset price at the end when starting the operation by purchasing the first investment product using all of the investment amount at the beginning and changing the investment target to the corresponding investment product each time the respective switching amounts are first reached, is provided.

[0014] Each of the information processing method and program of the first aspect of the present invention is each a method and program corresponding to the information processing apparatus of the first aspect of the present invention.

[0015] The information processing apparatus of the second aspect of the present invention In an information processing apparatus that calculates the probability distribution of the asset price at the end when operating with a given operation strategy, When an operation period, a target amount, an investment amount at the beginning, a function that returns an index of an investment product that takes a value in the closed interval [0, 1] from the amount from the investment amount at the beginning to the target amount (continuous value), and a set of parameters when the price fluctuations of a continuous number of 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 semi-open interval [0, ∞) from an amount greater than or equal to the investment amount at the beginning (continuous value), and a set of parameters when the price fluctuations of a continuous number of investment products indexed in the semi-open interval [0, ∞) are regarded as geometric Brownian motion are given, the probability distribution calculation means for calculating the probability distribution of the asset price at the end when starting the operation by purchasing the first investment product using all of the investment amount at the beginning and changing the investment target to the corresponding investment product each time the respective switching amounts are first reached, is provided.

[0016] Each of the information processing method and program of the second aspect of the present invention is each a method and program corresponding to the information processing apparatus of the second aspect of the present invention.

[0017] The information processing apparatus according to the third aspect of the present invention is in an information processing apparatus that optimizes parameters of an operation strategy for maximizing or minimizing a given evaluation index, when a quantitative evaluation index, an operation period, an investment amount at the beginning of the period, N switching amounts (N is an integer value of 1 or more), and parameters when the price fluctuations of N + 1 investment products corresponding to the start time of operation and the switching amounts are regarded as geometric Brownian motion are given, the operation starts by purchasing the first investment product using all of the 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. Parameter optimization means for optimizing the parameters of the operation strategy for maximizing or minimizing the evaluation index for this case, is provided.

[0018] The information processing method and program according to the third aspect of the present invention are the method and program corresponding to the information processing apparatus according to the third aspect of the present invention, respectively.

[0019] The information processing apparatus according to the fourth aspect of the present invention is in an information processing apparatus that optimizes parameters of an operation strategy for maximizing or minimizing a given evaluation index, A function that returns an index of an investment product that takes values in the closed interval [0, 1] from a quantitative evaluation index, an operation period, a target amount, an investment amount at the beginning, and an amount (continuous value) from the investment amount at the beginning to the target amount, and a set of parameters when the price fluctuations of a continuous number of 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 values in the semi-open interval [0, ∞) from an amount (continuous value) greater than or equal to the investment amount at the beginning, and a set of parameters when the price fluctuations of a continuous number of investment products indexed in the semi-open interval [0, ∞) are regarded as geometric Brownian motion, when given, start the operation by purchasing the first investment product using all of the investment amount at the beginning, and when performing an operation of changing the investment target to the corresponding investment product each time the switching amount is first reached, a parameter optimization means for optimizing the parameters of the operation strategy that maximizes or minimizes the evaluation index. comprises.

[0020] Each of the information processing method and program according to the fourth aspect of the present invention is each a method and program corresponding to the information processing apparatus according to the fourth aspect of the present invention.

Effect of the Invention

[0021] The present invention is an investment strategy proposed to solve the above-described conventional problems, and can specifically provide an investment strategy for improving a given evaluation index at the beginning of the operation.

Brief Description of the Drawings

[0022]

Figure 1

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Figure 15

Embodiments for Carrying Out 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 - Locking Type Operation> First, consider the probability distribution of the asset price at the end when operating with profit - locking type operation. Hereinafter, the probability distribution of the asset price at the end will be referred to as the end - of - period asset price probability distribution. The investment amount at the beginning will be referred to as the initial investment amount hereinafter. Figure 1 is a flowchart showing the operation process of profit lock - type operation. First, at the start of the operation, investment product 0 is purchased with the initial investment amount. Then, the operation is carried out for a certain period (S1), it is checked whether the operation period has ended (S2). If not, it is checked whether the target amount has been reached (S3). If not, the operation for a certain period (S1) is carried out again and the check for reaching the target is repeated. If it has been reached, re - allocation from the held investment product 0 to investment product 1 is implemented (S4), the operation is carried out for a certain period (S5), and the check for whether the operation period has ended (S6) is repeated to continue the operation. The re - allocation can be in the form of selling all of investment product 0 and purchasing investment product 1, or in the form of buying and selling the difference if the investment product is a portfolio consisting of multiple financial products.

[0025] Consider calculating the probability distribution of the end - of - period asset price for profit lock - type operation. Hereinafter, it is assumed that the check for reaching the target amount is carried out at any time and the opening of a certain period is not considered. This is considered to be a reasonable approximation when the operation period is sufficiently long with respect to a certain period.

[0026] It is considered that the asset price S of each investment product follows a geometric Brownian motion represented by the following formula.

Equation

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

[0028] If the initial investment amount is a value S different from 1 Init When it is, if the initial investment amount is 1 and the target amount is S G / S Init becomes, and when the probability variable of the end - of - period asset evaluation amount in another new profit - lock type operation with other variables the same is set as X, the probability variable of the end - of - period asset evaluation amount in the original operation is S Init can be written as X. Therefore, discussing only the case where the initial investment amount is 1 does not lack generality.

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

[0030] The contribution to the probability density function when the target amount is not reached can be calculated by the following formula.

Equation

[0031] Here, f LN is the probability density function of the log - normal distribution and is expressed by the following formula.

Equation

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

Equation

[0033] Here, f IG is the probability density function of the inverse - Gaussian distribution and is expressed by the following formula.

Equation

[0034] Considering equations (2) and (4) together, the probability density function p(S) of the end - of - period asset price probability distribution in the profit - lock type operation can be calculated as follows.

Equation

[0035] <Probability Distribution of Two - Point Switching Type Operation> Next, consider an operation in which two amounts for switching investment products are set. Hereafter, this operation will be referred to as the two - point switching type operation, and the amounts for switching investment products will be referred to as switching amounts. The two - point switching type operation can also be considered as an extension of the profit - lock type operation in which, by setting the larger switching amount as the target amount, switching to a third investment product is made at an amount lower than the target amount. Figure 2 is a flowchart showing the operation process of the two - point switching type operation. First, at the start of the operation, investment product 0 is purchased with the initial investment amount. Then, the operation is carried out for a certain period (S11), it is checked whether the operation period has ended (S12). If not, it is checked whether the switching amount has been reached (S13). If not, the operation for a certain period (S11) is carried out again and the check for reaching is repeated. If it has been reached, reallocation from the held investment product 0 to investment product 1 is implemented (S14). Then, the operation is carried out for a certain period (S15), it is checked whether the operation period has ended (S16). If not, it is checked whether the target amount has been reached (S17). If not, the operation for a certain period (S15) is carried out again and the check for reaching is repeated. If it has been reached, reallocation from the held investment product 1 to investment product 2 is implemented (S18), the operation is carried out for a certain period (S19), and the check for whether the operation period has ended (S20) is repeated to continue the operation.

[0036] Consider calculating the end - of - period asset price probability distribution of the two - point switching type operation. Similar to the profit - lock type operation, the check for reaching the switching amount is carried out at any time, and the consideration of a certain period opening is not taken into account.

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

[0038] The probability density function of the end - of - period asset price probability distribution in the two - point switching operation is calculated separately for the case where the first switching amount 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).

Equation

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

Equation

[0041] Considering Equations (7) and (8) together, the probability density function p(S) of the end - of - period asset price probability distribution in the two - point switching operation can be calculated as follows.

Equation

[0042] <Probability Distribution of N - point Switching - type Operation (in the case of recursive calculation)> Consider an operation with N switching amounts according to the same idea. Hereafter, this operation will be called N - point switching - type operation. Figure 3 is a flowchart showing the operation flow of the N - point switching - type operation. 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 checked whether the operation period has ended (S33). If not, it is checked 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 check for 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 checked whether K is N (S37). If not, the operation for a certain period (S32) is carried out again and the check for reaching is repeated. If K is N, the operation is carried out for a certain period (S38) and the check whether the operation period has ended (S39) is repeated to continue the operation.

[0043] Consider calculating the probability distribution of the end - of - period asset price of the N - point switching - type operation. Similar to before, the check for 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 operation, let the initial investment amount be 1, the K - th switching amount be S K and the operation period be t G and the drift of investment product K be μ K , the volatility be σ K . 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 operation, the probability density function of the end - of - period asset price probability distribution of the N - point switching - type operation 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] ···(10)

[0047] In the N - 1 switching type operation, with the initial investment amount set to 1, the K - th switching amount set to S K+1 / S1, the operation period set to t, and the drift of investment product K set to μ K+1 , volatility set to σ K+1 , let the probability density function of the terminal asset price probability distribution be p N-1 (S; t). The contribution to the probability density function when the first switching amount is reached can be calculated as follows using the convolution of the probability density function of the time until reaching and the probability density function p N-1 (S; t) of the terminal asset price probability distribution of the above N - 1 switching type operation. However, when N = 3, use the probability density function of the terminal asset price probability distribution of the aforementioned two - point switching type operation as p2(S; t). [Number] ···(11)

[0048] Considering Equations (10) and (11) together, the probability density function p(S) of the terminal asset price probability distribution of the N - point switching type operation can be calculated as follows. [Number] ···(12)

[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 end-of-period asset price probability distribution of the (N - 1)-point switching strategy type 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 directly calculating the probability density function of the end-of-period 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 end-of-period 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 times at each switching amount, then calculate the convolution with the probability density function of the end-of-period asset price probability distribution due to subsequent price transitions, 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 set to 1 for convenience. S k ≦ S k+1 ≦ S N From this, κ k takes values in the closed interval [0, 1].

Number

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

Number

[0054] κ k is used to define A k , B k as follows.

Number

Number

Number

[0055] Using the above parameters, the k-th switching amount can be calculated as follows.

Number

[0056] Consider a method of calculating the probability distribution of the arrival time at the N-th switching amount using the switching amounts parameterized by the above method.

[0057] The probability distribution p fht 1 (t) of the arrival time at the first switching amount is the probability distribution of the arrival time of geometric Brownian motion, so it can be calculated as follows using the inverse Gaussian distribution.

Number

[0058] The arrival time at the second switching amount is the sum of the arrival time at the first switching amount and the time from reaching the first switching amount to reaching the second switching amount. Therefore, it can be calculated as follows using the convolution of the probability density functions of the inverse Gaussian distribution.

Number

[0059] Since the above formula cannot be calculated analytically, when actually performing numerical calculations, from 0 to the operation period t G The interval up to is evenly divided, and the value is obtained by numerically integrating the above formula at each point and approximated by a piecewise linear function obtained by linear interpolation. However, when A k is small, f IG approaches the delta function and cannot be approximated well. Therefore, an appropriate threshold is determined, and when A k is below that, f IG during the calculation can be regarded as the delta function and calculated accordingly. In this case, p fht k (t) = p fht k-1 (t).

[0060] By repeating the same idea, the (k + 1)-th probability distribution can be calculated as follows using the k-th probability distribution.

Equation

[0061] Using the probability distribution of the time to reach the N-th switching amount above, the probability density function of the end-of-period asset price probability distribution in the N-point switching operation can be When not reaching the first switching amount When reaching the k-th switching amount but not reaching the (k + 1)-th switching amount When reaching the last switching amount calculated by dividing it into three major cases.

[0062] First, the contribution to the probability density function when not reaching the first switching amount can be calculated by the following formula in the same way as formula (10).

Equation

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

Number

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

Number

[0065] Combining Equation (22), Equation (23), and Equation (24), the probability density function of the terminal asset price probability distribution in the N-point switching type operation can be calculated by the following formula.

Number

Example

[0066] In this example, in the 5-point switching type 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 (25) are calculated and compared. The parameters of the 5-point switching type operation are an initial investment amount of 1, and the switching amounts are 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 operation period is 10 years, and each investment product 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), and the volatility is 0.577% (monthly rate). Let it be so. Monte Carlo simulation generates samples according to the flowchart in Figure 3. Assume that the number of samples is 1 million, the operation period is 1 month, and the monthly return follows a normal distribution with the drift of the investment product as the expected value and the volatility as the volatility. Figure 4 shows a bar graph that overlays the line graph according to Equation (25) and the results of the Monte Carlo simulation as a histogram with 100 bins. 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.

[0067] <Regarding the conditions for accurately calculating the probability distribution of the time to reach the switching amount> In the above calculation method, the calculation of the probability distribution of the time to reach the k-th switching amount approximates with a piecewise linear function, so the calculation accuracy depends on the approximation accuracy. However, when the drift and volatility of the investment product satisfy a specific relationship, it is possible to perform an exact calculation without performing an approximate calculation due to the reproductive property of the inverse Gaussian distribution. Three conditions under which such a calculation is possible are shown below.

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

Equation

[0069] At this time, the probability density function of the time to reach the k-th switching amount can be calculated as follows.

Number

[0070] Next, assume that the drift and volatility of the investment product satisfy the relationship

Number

[0071] At this time, the probability density function of the probability distribution of the time to reach the k-th switching amount can be calculated as follows.

Number

[0072] Finally, assume that the drift and volatility of the investment product satisfy the relationship

Number

[0073] At this time, the probability density function of the probability distribution of the time to reach the k-th switching amount can be calculated as follows.

Number

[0074] Combining the above, the probability density function of the end - of - period asset price probability distribution for the N - point switching operation can be calculated according to the flowchart shown in Figure 5. First, prepare the values of the parameters required for the calculation (S41). If the probability density function of the end - of - period asset price probability distribution for the (N - 1) - point switching operation required for the calculation has been obtained (S42), use Equation (12) for the calculation (S43). If it has not been obtained, check whether the investment product satisfies the condition for the exact calculation of the probability distribution of the switching amount arrival time (S44). If not, calculate the probability density function of the arrival time up to each switching amount by the aforementioned approximate method (S45). If it is satisfied, calculate the probability density function of the arrival time up to each switching amount by any of the exact methods of Equation (27), Equation (29), or Equation (31) (S46). Then, calculate the contribution when the switching amount has never been reached (S47), the contribution when the k - th switching amount has been reached but the (k + 1) - th switching amount has not been reached (S48), and the contribution when the last switching amount has been reached (S49), and sum up each contribution (S50) to calculate the probability density function of the end - of - period asset price probability distribution for the N - point switching operation.

Example

[0075] In this example, the calculation speeds are compared between the case of calculating the probability density function of the end - of - period asset price probability distribution for the N - point switching operation by an approximate method and the case of exact calculation by Equation (31) when the aforementioned conditional formula (30) is satisfied. The parameters of the N - point switching operation are set such that the initial investment amount is 1, the operation period is 10 years, the switching amounts are equally divided into N parts between 1.0 and 2.0, the volatility of the investment product is equally divided into N parts from 0.577% (monthly rate) to 2.887% (monthly rate), the drift is calculated by Equation (30) with SR = 0.261, and the investment products are corresponded to in order from the one with the highest volatility. Figure 6 is a diagram comparing the speeds of calculation in an approximate method and in an exact calculation when the number of switching amounts is changed from 10 to 100. The multiples of the calculation time taken in each case are plotted with the calculation time in the exact 10-point switching strategy set to 1. It can be seen that in addition to the fact that there is no need for approximation in the exact case, the speed is faster because there is no need to calculate numerical integration. However, it should be noted that the exact calculation can only be used when the investment product meets the corresponding conditions.

[0076] <Probability Distribution of Continuous Switching Type Operation> As the limit of making N in the N-point switching type operation extremely large, an operation using continuous switching amounts can be considered. Hereafter, this operation will be referred to as continuous switching type operation. The continuous switching type operation can be divided into two types: the case where the range of the switching amount is bounded and the case where it is unbounded. The case where it is bounded will be called bounded continuous switching type operation, and the case where it is unbounded will be called unbounded continuous switching type operation. Figure 7 is a flowchart showing the operation flow of the continuous switching type operation. First, at the start of the operation, investment product 0 is purchased with the initial investment amount, and the variable S representing the past highest amount high is assigned the initial investment amount S Init (S61). Then, the operation is carried out for a certain period (S62), it is confirmed whether the operation period has ended (S63), and if not, it is confirmed whether the asset evaluation amount S at that time is higher than S high (S64). If not, the operation for a certain period (S62) is carried out again and the confirmation of the asset evaluation amount is repeated. If it is higher, it is confirmed whether it is an unbounded continuous switching type operation (S65), and if not, it is confirmed whether S is higher than the target amount S G (S66). If not, a reallocation from the investment product being operated to the investment product corresponding to S is carried out (S67), S high is assigned S (S68), and the operation for a certain period (S62) is carried out again and the confirmation of the asset evaluation amount is repeated. If it is a bounded continuous switching type and S is higher than S G (S66), the operation for a certain period is carried out (S69) and the confirmation of whether the operation period has ended (S70) is repeated to continue the operation.

[0077] Consider calculating the probability distribution of the end - of - period asset price for continuous switching operations. As 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.

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

[0079] Calculate the probability density function of the end - of - period asset price probability distribution for the bounded continuous switching operation by dividing it into the case where the target amount is not reached and the case where it is reached.

[0080] The contribution to the probability density function when the target amount is not reached can be calculated by the following formula.

Equation

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

Equation

[0082] The contribution to the probability density function when the target amount is reached can be written by the following formula.

Number

[0083] Combining Equation (32) and Equation (34), the probability density function of the end - of - period asset price probability distribution of the bounded continuous switching type operation can be calculated as follows.

Number

[0084] Next, consider the unbounded continuous switching type operation. As parameters in the unbounded continuous switching type operation, assume the initial investment amount is 1, the operation period is t G and z(S) is a function from the semi - open interval [1, ∞) to the semi - open interval [0, ∞) that returns the index of the investment product at each amount, and μ(z), σ(z) are functions that return the drift and volatility of the corresponding investment product from the index of the investment product (semi - open interval [0, ∞)).

[0085] The probability density function of the end - of - period asset price probability distribution of the unbounded continuous switching type operation can be calculated as follows.

Number

[0086] Combining the above, the probability density function of the end - of - period asset price probability distribution of the continuous switching type operation can be calculated according to the flowchart shown in Figure 8. First, prepare the values of the parameters required for the calculation (S81), and calculate the probability density function of the arrival time to each asset price according to Equation (33) (S82). If it is not a bounded continuous switching type operation (S83), calculate the probability density function using Equation (36) (S84). Otherwise, calculate the contribution when the target amount is not reached (S85) using Equation (32) and the contribution when the target amount is reached (S86) using Equation (34), and sum up the respective contributions (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 are generated for the Monte Carlo simulation according to the flowchart of FIG. 7. It is assumed that the number of samples is 1 million, the operation for a certain period is 1 month, and 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 result of the Monte Carlo simulation are shown as a bar graph in a histogram with 100 bins and overlaid. 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 result 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 result being affected by noise, an inefficient method such as grid search needs to be used to obtain the optimal parameters under the given evaluation index. 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 an indicator for quantitative evaluation is the probability of achieving the target amount. This is the target amount S G and can be calculated as follows using the probability density function p(S) of the end-of-period asset price probability distribution of the N-point switching operation.

Equation

[0090] Another example of an indicator for quantitative evaluation is a method of evaluation using prospect theory. The method of evaluating a continuous probability distribution using prospect theory is carried out as follows.

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

[0092] At this time, the evaluation indicator in prospect theory can be calculated by the following formula.

Equation

[0093] In prospect theory, the value function and the probability weighting function are not determined and there is arbitrariness in the choice. In particular, when evaluating an unbounded and continuously valued object such as the probability distribution of asset prices, Non-Patent Document 2 points out that using the piecewise power function proposed by Tversky and Kahneman in Non-Patent Document 1, which is the commonly used value function, will cause the St. Petersburg paradox. Therefore, when evaluating the probability distribution of the end-of-period asset price of the N-point switching type operation, it is calculated using the piecewise exponential function type value function proposed by Giorgi and Hens in Non-Patent Document 2.

[0094] When calculating the evaluation index in prospect theory, it is necessary to calculate the cumulative distribution function of the probability distribution of the end-of-period asset price of the N-point switching strategy type. From the definition of the cumulative distribution function, it can be seen that it can be calculated in three cases as follows.

Equation

[0095] First, P1(X) can be calculated by the following formula.

Equation

[0096] Next, P2 k (X) can be calculated by the following formula.

Equation

[0097] Finally, P3(X) can be calculated by the following formula.

Equation

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

Number

[0099] In the calculation of the cumulative distribution function of the end - of - period asset price probability distribution of the above - mentioned N - point switching strategy type, it is necessary to calculate all the contributions from the switching amounts lower than the asset price of the argument. However, when calculating the evaluation index based on prospect theory by numerical integration, it is considered that the number of times of evaluating the cumulative distribution function at points higher than the switching amount will increase. Since the calculation of the complementary cumulative distribution function only calculates the contributions from the switching amounts higher than the argument, when calculating the evaluation index based on prospect theory by numerical integration, it is considered that it is more computationally efficient to calculate in a form using the complementary cumulative distribution function.

[0100] When writing the complementary cumulative distribution function of X 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 by the following equation.

Number

[0102] The complementary cumulative distribution function of the end - of - period asset price probability distribution of the N - point switching strategy type becomes the following equation from the definition, and it can be seen that it can be calculated in three cases similar to the cumulative distribution function.

Number

[0103] First, the cumulative distribution function of the N-point switching strategy type's end-of-period asset price probability distribution can be calculated by the following formula (the cumulative distribution function of P with a macron means the P with a bar on top. The same applies hereinafter). [Number] ···(47)

[0104] Next, the cumulative distribution function of P2 with a macron k (X) can be calculated by the following formula. [Number] ···(48)

[0105] Finally, the cumulative distribution function of P3(X) with a macron can be calculated by the following formula. [Number] ···(49)

[0106] Summarizing the above, the complementary cumulative distribution function of the N-point switching strategy type's end-of-period asset price probability distribution can be calculated as follows. [Number] ···(50)

[0107] As the last example of the index for quantitative evaluation, the m-th moment around the target amount can be mentioned. The target amount is S G The m-th moment around it can be calculated as follows from the definition. [Number] ···(51)

[0108] The m-th moment around the target amount can be calculated as follows using the moments up to the m-th moment around the origin. [Number] ···(52)

[0109] The m-th moment around the origin can be calculated in three cases according to the following formula, as can be seen from the definition.

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 expressed by the following formula.

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] If quantitative evaluation indices are given as described above, they can be calculated analytically. Therefore, the parameters of the operation strategy (some or all of the operation period and switching amount) that maximize or minimize the given evaluation indices can be obtained by an optimization method.

[0116] In particular, since the formula for the probability distribution of the end - of - period asset price of the N - point switching strategy type is differentiable with respect to the operation period and the switching amount, when the evaluation index is also differentiable, it can be optimized using an optimization method that uses gradient information, such as the gradient descent method or the quasi - Newton method (BFGS method). The derivative with respect to each parameter can be obtained analytically, but it is also possible to calculate it from the program using automatic differentiation.

[0117] When it takes time to evaluate the derivative by the aforementioned automatic differentiation, or when the evaluation index is not differentiable in the first place, it is also possible to consider an optimization method that does not use gradient information, such as a genetic algorithm or CMA - ES.

[0118] Summarizing the above optimization framework into a flowchart, it can be calculated according to a flowchart as shown in Figure 10. First, a quantitative evaluation index is given (S91). Next, parameters that are not subject to optimization are given (S92), and initial values of the parameters 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, when it is not differentiable or the calculation cost of the derivative is high, optimization is performed using an optimization method that does not require gradient information (S96). As a result of the optimization, the optimized parameters are obtained (S97).

Example

[0119] In this embodiment, the optimization of the switching amount of the N-point switching type operation is actually performed using the second moment around the target amount as an evaluation index. Since it can be interpreted that the closer the value of the evaluation index is to zero, the more the end-of-period asset price is distributed around the target amount, the optimization is performed so that the evaluation index becomes smaller. The parameters of the N-point switching type operation are such that the initial investment amount is 1, the target amount is 2, the operation period is 10 years, the switching amount has the last switching amount fixed to the target amount, and the other values are obtained by optimization. The volatility of the investment product is equally divided from 0.866% (monthly rate) to 2.598% (monthly rate), the drift is calculated by Equation (30) with SR = 0.280, and the investment products are assigned in descending order of volatility. The initial value of the switching amount is set in such a way that the target amount is equally divided by N from the initial investment amount. The CMA-ES is used as the optimization method. Fig. 11 shows the transition of the values 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. Fig. 12 shows the values of the switching amount, which is the optimization result in the case of the 20-point switching strategy. It can be confirmed that the risk level gradually decreases from around 1.5, which is before the target amount.

[0120] <Optimization Method for Continuous Switching Type Operation> Similar to the N-point switching type operation, in the continuous switching type operation, since the probability density function of the end-of-period asset price probability distribution can be obtained analytically, when an index for quantitatively evaluating the end-of-period 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.

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

Equation

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

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

[0124] The information processing apparatus 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 storage 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. In the RAM 13, data and the like necessary for the CPU 11 to execute various processes are also appropriately stored.

[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 storage 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 types of information. The input unit 17 is composed of various hardware buttons and the like, and inputs various types of information. The storage unit 18 is composed of a DRAM (Dynamic Random Access Memory) or the like, and stores various types of data. The communication unit 19 controls communication with other devices via a network including the Internet.

[0128] The drive 20 is provided as necessary. A removable medium 30 made of a magnetic disk, an optical disk, a magneto-optical disk, or a semiconductor memory or the like is appropriately mounted on the drive 20. The program read from the removable medium 30 by the drive 20 is installed in the storage unit 18 as necessary. Also, the removable medium 30 can store various types of data stored in the storage unit 18 in the same manner as the storage unit 18.

[0129] [Functional Configuration] Next, the functions of the information processing apparatus 1 will be described with reference to FIG. 15. FIG. 15 is a functional block diagram showing an example of the functional configuration of the information processing apparatus 1 in FIG. 14.

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

[0131] In the case of the first mode where the information processing apparatus 1 calculates the probability distribution of the asset price at the end of the period when operating with a given operation strategy, the probability distribution calculation unit 51 functions as follows in the CPU 11. That is, when the probability distribution calculation unit 51 is given the operation period, the investment amount at the beginning of the period, N switching amounts (N is an integer value of 1 or more), and the parameters when the price fluctuations of N + 1 investment products corresponding to the start time of operation and the switching amounts are regarded as geometric Brownian motion, it purchases the first investment product using all of the investment amount at the beginning of the period and starts operation, and for the case of performing an operation of changing the investment target to the corresponding investment product each time the respective switching amounts are first reached, it executes the calculation of the probability distribution of the asset price at the end of the period.

[0132] Here, the probability distribution calculation unit 51 can execute the above calculation when the parameters when regarding the price fluctuations of the investment products as the geometric Brownian motion satisfy specific conditions. As a result, a simpler and faster calculation can be executed as the above calculation.

[0133] Also, in the case of the second mode where the information processing apparatus 1 calculates the probability distribution of the asset price at the end of the period when operating with a given operation strategy, the probability distribution calculation unit 51 functions as follows in the CPU 11. That is, when the probability distribution calculation unit 51 is given an operation period, a target amount, an investment amount at the beginning, a function that returns an index of an investment product that takes values in the closed interval [0, 1] from the investment amount at the beginning to the target amount (continuous value), and a set of parameters when the price fluctuations of a continuous number of 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 values in the semi-open interval [0, ∞) from an amount (continuous value) greater than or equal to the investment amount at the beginning, and a set of parameters when the price fluctuations of a continuous number of investment products indexed in the semi-open interval [0, ∞) are regarded as geometric Brownian motion, it starts the operation by purchasing the first investment product using all of the investment amount at the beginning, and calculates the probability distribution of the asset price at the end for the case where the investment target is changed to the corresponding investment product each time the respective switching amount is first reached.

[0134] Also, in the case of the third aspect where the information processing apparatus 1 optimizes the parameters of an operation strategy that maximizes or minimizes a given evaluation index, the parameter optimization unit 52 functions as follows in the CPU 11. That is, when the parameter optimization unit 52 is given a quantitative evaluation index, an operation period, an investment amount at the beginning, N switching amounts (N is an integer value of 1 or more), and parameters when the price fluctuations of N + 1 investment products corresponding to the start time of the operation and the switching amounts are regarded as geometric Brownian motion, it starts the operation by purchasing the first investment product using all of the investment amount at the beginning, and optimizes the parameters of the operation strategy that maximizes or minimizes the evaluation index for the case where the investment target is changed to the corresponding investment product each time the respective switching amount is first reached.

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

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

[0137] Also, in the case of the fourth aspect where the information processing apparatus 1 optimizes the parameters of an operation strategy that maximizes or minimizes a given evaluation index, the parameter optimization unit 52 functions as follows in the CPU 11. That is, when the parameter optimization unit 52 is given a quantitative evaluation index, an operation period, a target amount, an investment amount at the beginning, an index of an investment product that takes a value in the closed interval [0, 1] from the investment amount at the beginning to the target amount (continuous value), and a set of parameters when the price fluctuations of a continuous number of investment products indexed in the closed interval [0, 1] are regarded as geometric Brownian motion, or an index of an investment product that takes a value in the semi-open interval [0, ∞) from an amount (continuous value) greater than or equal to the investment amount at the beginning, and a set of parameters when the price fluctuations of a continuous number of investment products indexed in the semi-open interval [0, ∞) are regarded as geometric Brownian motion, it starts the operation by purchasing the first investment product using all of the investment amount at the beginning, and performs an operation of changing the investment target to the corresponding investment product each time the switching amount is first reached, and optimizes the parameters of the operation strategy that maximizes or minimizes the evaluation index for this case.

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

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

[0140] As described above, one embodiment of the present invention has been described. However, the present invention is not limited to the above-described embodiment, and modifications, improvements, etc. within the scope that can achieve 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] Also, 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 capable of executing the above-described series of processes as a whole, and the functional blocks used for realizing this function are not particularly limited to the example of FIG. 15.

[0143] Also, the location where the functional blocks exist is not limited to FIG. 15 and may be arbitrary. Also, one functional block may be configured by hardware alone, software alone, or a combination thereof.

[0144] When the processing of each functional block is executed by software, the program constituting the software is installed in a computer or the like from a network or a recording medium. The computer may be a computer incorporated in dedicated hardware. Also, the computer may be a computer capable of executing various functions by installing various programs, for example, a general-purpose smartphone or personal computer in addition to a server.

[0145] A recording medium containing such a program is not only composed of a removable medium distributed separately from the apparatus main body in order to provide the program to each user, but also composed of a recording medium or the like provided to each user in a state pre-installed in the apparatus main body.

[0146] In addition, in this specification, the steps of describing the program recorded on the recording medium include not only the processes performed in chronological order according to the order, but also the processes executed in parallel or individually even if they are not necessarily processed in chronological order.

[0147] Also, in this specification, the term "system" means the entire apparatus composed 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 may have the following configuration and can take various embodiments.

[0149] That is, the information processing apparatus (for example, the information processing apparatus 1 in FIG. 13) according to the first aspect to which the present invention is applied is In an information processing apparatus that calculates the probability distribution of the asset price at the end of the period when operating with a given operation strategy, When an operation period, an investment amount at the beginning of the period, N switching amounts (N is an integer value of 1 or more), and parameters when the price fluctuations of N + 1 investment products corresponding to the start time of operation and the switching amounts are regarded as geometric Brownian motion are given, the first investment product is purchased using all of the investment amount at the beginning of the period to start the operation, and the probability distribution calculation means (for example, the probability distribution calculation unit 51 in FIG. 14) that executes the calculation of the probability distribution of the asset price at the end of the period for the case of performing an operation of changing the investment target to the corresponding investment product each time the respective switching amounts are first reached. Comprising.

[0150] The probability distribution calculation means executes the calculation for the case where the parameter when regarding the price fluctuation of the investment product as the geometric Brownian motion satisfies a specific condition. It can be done. Thereby, as the calculation, a simpler and faster calculation can be executed.

[0151] Also, an information processing apparatus according to a second aspect to which the present invention is applied (for example, the information processing apparatus 1 in FIG. 13) In an information processing apparatus that calculates the probability distribution of the asset price at the end of the period when operating with a given operation strategy, When an operation 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 from the investment amount at the beginning of the period to the target amount (continuous value), and a set of parameters when regarding the price fluctuations of a continuous number of investment products indexed in the closed interval [0, 1] as geometric Brownian motion, or a function that returns an index of an investment product that takes a value in the semi-open interval [0, ∞) from an amount greater than or equal to the investment amount at the beginning of the period (continuous value), and a set of parameters when regarding the price fluctuations of a continuous number of investment products indexed in the semi-open interval [0, ∞) as geometric Brownian motion are given, the operation starts by purchasing the first investment product using all of the investment amount at the beginning of the period, and the probability distribution calculation means (for example, the probability distribution calculation unit 51 in FIG. 14) that executes the calculation of the probability distribution of the asset price at the end of the period for the case where the investment target is changed to the corresponding investment product each time the switching amount is first reached. It includes.

[0152] Also, an information processing apparatus according to a third aspect to which the present invention is applied (for example, the information processing apparatus 1 in FIG. 13) In an information processing apparatus that optimizes the parameters of an operation strategy so as to maximize or minimize a given evaluation index, When a quantitative evaluation index, an operation period, an initial investment amount, N switching amounts (where N is an integer value of 1 or more), and parameters when the price fluctuations of N + 1 investment products corresponding to the start of operation and the switching amounts are regarded as geometric Brownian motion are given, when starting operation by purchasing the first investment product using all of the initial investment amount and changing the investment target to the corresponding investment product each time the respective switching amounts are first reached, for the case of performing operation, a parameter optimization means (for example, the parameter optimization unit 52 in FIG. 14) that optimizes the parameters of the operation strategy that maximizes or minimizes the evaluation index, is provided.

[0153] The parameter optimization means optimizes some or all of the operation period and the switching amount as the parameters of the operation strategy that maximizes or minimizes the evaluation index. This can be done.

[0154] As the evaluation index, the utility based on the cumulative prospect theory can be used. This can be done. Thereby, it becomes possible to suppress the amount of calculation and reduce numerical instability.

[0155] Also, the information processing apparatus according to the fourth aspect to which the present invention is applied (for example, the information processing apparatus 1 in FIG. 13) In an information processing apparatus that optimizes the parameters of an operation strategy that maximizes or minimizes a given evaluation index, A function that returns an index of an investment product that takes values in the closed interval [0, 1] from a quantitative evaluation index, an operation period, a target amount, an investment amount at the beginning, and an amount (continuous value) from the investment amount at the beginning to the target amount, and a set of parameters when the price fluctuations of a continuous number of 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 values in the semi-open interval [0, ∞) from an amount (continuous value) greater than or equal to the investment amount at the beginning, and a set of parameters when the price fluctuations of a continuous number of investment products indexed in the semi-open interval [0, ∞) are regarded as geometric Brownian motion. When given, start the operation by purchasing the first investment product using all of the investment amount at the beginning, and when each switching amount is first reached, change the investment target to the corresponding investment product. For the case of performing the operation, a parameter optimization means (for example, the parameter optimization unit 52 in FIG. 14) that optimizes the parameters of the operation strategy that maximizes or minimizes the evaluation index, is provided.

[0156] The parameter optimization means optimizes some or all of the operation period and the switching amount as the parameters of the operation strategy that maximizes or minimizes the evaluation index. This can be done.

Explanation of Signs

[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. In an information processing apparatus that optimizes parameters of an operation strategy for maximizing or minimizing a given evaluation index, when a quantitative evaluation index, an operation period, an investment amount at the beginning of the period, N switching amounts (N is an integer value of 1 or more), and parameters when the price fluctuations of N + 1 investment products corresponding to the start time of the operation and the switching amounts are regarded as geometric Brownian motion are given, the operation starts by purchasing the first investment product using all of the 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. Parameter optimization means for optimizing the parameters of the operation strategy for maximizing or minimizing the evaluation index for this case, An information processing apparatus comprising the same.

2. The parameter optimization means optimizes some or all of the operation period and the switching amount as the parameters of the operation strategy for maximizing or minimizing the evaluation index. The information processing apparatus according to claim 1.

3. Using the utility based on the cumulative prospect theory as the evaluation index, The information processing apparatus according to claim 1 or 2.

4. In an information processing method executed by an information processing apparatus that optimizes parameters of an operation strategy for maximizing or minimizing a given evaluation index, when a quantitative evaluation index, an operation period, an investment amount at the beginning of the period, N switching amounts (N is an integer value of 1 or more), and parameters when the price fluctuations of N + 1 investment products corresponding to the start time of the operation and the switching amounts are regarded as geometric Brownian motion are given, the operation starts by purchasing the first investment product using all of the 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. A parameter optimization step for optimizing the parameters of the operation strategy for maximizing or minimizing the evaluation index for this case, An information processing method including the same.

5. In a computer that optimizes parameters of an operation strategy for maximizing or minimizing a given evaluation index, When a quantitative evaluation index, an operation period, an initial investment amount, N switching amounts (N is an integer value of 1 or more), and parameters when the price fluctuations of N+1 investment products corresponding to the operation start time and the switching amounts are regarded as geometric Brownian motion are given, the operation starts by purchasing the first investment product using all of the initial investment amount, and the investment target is changed to the corresponding investment product each time each switching amount is first reached. A parameter optimization step for optimizing the parameters of an operation strategy that maximizes or minimizes the evaluation index, A program for executing control processing including this.

6. In an information processing apparatus that optimizes the parameters of an operation strategy that maximizes or minimizes a given evaluation index, When a quantitative evaluation index, an operation period, a target amount, an initial investment amount, a function that returns an index of an investment product that takes a value in the closed interval [0, 1] from the amount from the initial investment amount to the target amount (continuous value), and a set of parameters when the price fluctuations of a continuous number of 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 semi-open interval [0, ∞) from an amount greater than or equal to the initial investment amount (continuous value), and a set of parameters when the price fluctuations of a continuous number of investment products indexed in the semi-open interval [0, ∞) are regarded as geometric Brownian motion are given, the operation starts by purchasing the first investment product using all of the initial investment amount, and the investment target is changed to the corresponding investment product each time each switching amount is first reached. Parameter optimization means for optimizing the parameters of an operation strategy that maximizes or minimizes the evaluation index, An information processing apparatus comprising this.

7. The parameter optimization means performs optimization of some or all of the operation period and the switching amount as the parameters of the operation strategy that maximizes or minimizes the evaluation index. The information processing apparatus according to claim 6.

8. In an information processing method executed by an information processing apparatus that optimizes the parameters of an operation strategy that maximizes or minimizes a given evaluation index, A parameter optimization step for optimizing the parameters of an operation strategy that maximizes or minimizes an evaluation index, for the case where, given a quantitative evaluation index, an operation period, a target amount, an investment amount at the beginning, a function that returns an index of an investment product that takes values in the closed interval [0, 1] from the investment amount at the beginning to the target amount (continuous value), and a set of parameters when the price fluctuations of a continuous number of 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 values in the semi-open interval [0, ∞) from an amount (continuous value) greater than or equal to the investment amount at the beginning, and a set of parameters when the price fluctuations of a continuous number of investment products indexed in the semi-open interval [0, ∞) are regarded as geometric Brownian motion, an operation is started by purchasing the first investment product using all of the investment amount at the beginning, and the investment target is changed to the corresponding investment product each time each switching amount is first reached. An information processing method including the above.

9. A computer for optimizing the parameters of an operation strategy that maximizes or minimizes a given evaluation index, A parameter optimization step for optimizing the parameters of an operation strategy that maximizes or minimizes an evaluation index, for the case where, given a quantitative evaluation index, an operation period, a target amount, an investment amount at the beginning, a function that returns an index of an investment product that takes values in the closed interval [0, 1] from the investment amount at the beginning to the target amount (continuous value), and a set of parameters when the price fluctuations of a continuous number of 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 values in the semi-open interval [0, ∞) from an amount (continuous value) greater than or equal to the investment amount at the beginning, and a set of parameters when the price fluctuations of a continuous number of investment products indexed in the semi-open interval [0, ∞) are regarded as geometric Brownian motion, an operation is started by purchasing the first investment product using all of the investment amount at the beginning, and the investment target is changed to the corresponding investment product each time each switching amount is first reached. A program for executing control processing including the above.

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