Non-exponential mixed asset portfolio optimization system

Abstract

The invention provides a non-exponential mixed asset portfolio optimization system, and relates to the field of portfolio optimization. Under the condition that external indexes are not introduced, heterogeneity between asset categories is processed, and a more excellent and more practical mixed asset portfolio is generated, so that investors are helped to make profits by constructing the mixed asset portfolio. Meanwhile, the provided improved artificial bee colony algorithm is used for solving the mixed asset investment portfolio, the solving efficiency of the mixed asset investment portfolio and the dispersion degree of solutions are improved by introducing external storage and improving a solution mining strategy in the bee colony algorithm, and therefore it is guaranteed that the optimal mixed asset investment portfolio can be efficiently generated.

Description

Technical Field

[0001] The present invention relates to the field of investment portfolio optimization, and in particular to a non-index mixed asset investment portfolio optimization system. Background Art

[0002] In recent years, mixed asset portfolios have gradually gained a foothold in the investment portfolio field. The development of mixed asset portfolios is driven by the trend of the financial sector from separate operations to mixed operations. In mixed operations, financial institutions such as banks and securities companies are allowed to provide investors with a variety of financial services, including deposits, securities, bonds and funds. By combining different types of assets, mixed asset portfolios provide better flexibility and a higher risk-return ratio. However, the introduction of multiple types of assets brings many challenges to the construction of mixed asset portfolios.

[0003] Among many challenges, the most important one is to deal with the heterogeneity between different asset classes. This heterogeneity leads to unacceptable errors when directly combining products from different asset classes. Take stocks and bonds as an example: first, bonds provide fixed interest, while the returns of stocks vary over time; second, bonds have a limited maturity date, while stocks are considered to never mature; finally, the price of bonds is mainly determined by future returns, while the price of stocks is more or less random. These differences require different categories of products to be managed independently in the mixed portfolio optimization problem, a conclusion that is recognized by most people.

[0004] To address this challenge, many representative index-based methods have been proposed. Index-based methods are considered to be the standard approach to solving mixed asset portfolio optimization. The outstanding performance of representative index-based methods mainly comes from their ability to handle heterogeneity between asset classes. Representative index-based methods deal with the mixed asset portfolio optimization problem through a two-stage process. The first stage optimizes the proportion of funds allocated to different asset classes. This stage is called the asset allocation stage. In this stage, suitable indexes are selected to represent asset classes. Finally, the best fund allocation scheme is obtained through optimization, that is, the funds invested in different asset classes. In the second stage, the funds of each asset class are allocated to the specific available products of the asset class. The portfolio constructed for each asset class in this stage should have the same expected return as the corresponding index in the first stage, so as to obtain the funds invested in different available products in each asset class and obtain the final mixed asset portfolio.

[0005] In recent years, the representative index-based approach has achieved considerable success, mainly because the representative index-based approach effectively avoids the direct combination of products between different asset classes through a two-stage structure, which effectively eliminates the impact of heterogeneity. However, despite its wide application, the index-based approach using indices to represent asset classes has been criticized by many. On the one hand, the index reflects the average return of the asset class, which means that information such as the maximum return and minimum risk of the asset class is usually discarded. The lack of information affects the comprehensiveness of the asset class representation, and thus affects the optimality of the reference investment. On the other hand, most indices represent the performance of a fixed set of products over a period of time. However, due to investor demand, the fixed set of products represented by the index is usually very different from the actual product, resulting in inconsistencies in the two stages. Summary of the invention

[0006] In view of the shortcomings of the prior art, the present invention provides a non-exponential mixed asset investment portfolio optimization system. The system adopts a non-exponential heterogeneity elimination method to formalize the mixed asset investment portfolio optimization problem as a multi-objective two-level optimization problem, and designs and implements an improved artificial bee colony algorithm to solve this problem, thereby constructing an optimal mixed asset investment portfolio.

[0007] A non-indexed mixed asset portfolio optimization system includes a data acquisition module, a data processing module, a problem construction module and a problem solving module;

[0008] The data acquisition module is used to acquire the historical market data of the pre-assembled products as input to the data processing module;

[0009] The data processing module is used to preprocess the historical market data of the pre-combined products, and classify the pre-processed historical market data of the pre-combined products according to asset categories, and obtain the historical market data of each asset category as the input of the problem construction module, and the historical market data of each asset category includes the expected rate of return of different products belonging to the asset category;

[0010] The problem construction module constructs a two-layer multi-objective optimization problem based on the historical market data of each asset class;

[0011] The problem solving module is used to solve the constructed two-level multi-objective optimization problem to obtain a mixed asset investment portfolio; the mixed asset investment portfolio includes the proportion of funds allocated to each asset category and the proportion of funds allocated to each product in each asset category;

[0012] Furthermore, the products include stock products, fund products, bond products and financial products;

[0013] For stock products, their historical market data include the highest price, lowest price, opening price and closing price of the stock products every day within a period of time; for fund products, their historical market data include the highest price, lowest price, opening price and closing price of the fund products every day within a period of time; for bond products, their historical market data include the expected rate of return at the time of issuance; for financial products, their historical market data include the expected rate of return in the historical earnings reports they have released;

[0014] Furthermore, the asset categories include: stocks, funds, bonds and financial products;

[0015] Furthermore, the preprocessing is: deleting or replacing abnormal values ​​in the historical market data of stock products and fund products, filling in missing values, and then calculating the expected rate of return of stock products and fund products based on the opening price and closing price;

[0016] Further, the two-layer multi-objective optimization problem includes an outer optimization task and a plurality of inner optimization tasks, each inner optimization task is used to obtain a plurality of candidate investment portfolios in an asset class, these candidate investment portfolios are Pareto optimal in terms of rate of return and risk, and each candidate investment portfolio includes a proportion of funds allocated to each product in the asset class; the outer optimization task is used to select an investment portfolio from the plurality of candidate investment portfolios in each asset class, and allocate funds to the asset class corresponding to each selected investment portfolio; the number of the inner optimization tasks is equal to the number of asset classes;

[0017] Furthermore, the inner optimization task f l (k) is expressed as:

[0018] max x T P k V k (1)

[0019] min x T P k cov(V k ,V k )x (2)

[0020]

[0021] Where x is a number with a length of N. k A vector representing the allocation to asset class C k Medium k The funding ratio of each product, x i is the element in vector x, indicating the distribution to N k The proportion of funds of the i-th product among the products, i is the product number, k is the asset category number and M is the number of asset classes, C k is the kth asset class, N k For asset class C k The number of products in k Is a diagonal matrix used to represent the investor's preferences. k If the element If it is 1, it means that the investor considers N k The i-th product among the products is included in the investment portfolio, and 0 is the opposite; V k For a saved asset class C k The matrix of historical market data of all products in , cov() is the covariance function, cov(V k ,V k ) indicates V k Its own covariance;

[0022] Furthermore, the outer optimization task is expressed as:

[0023]

[0024] u k ≥0,k=1,2,…,M (8)

[0025]

[0026] Among them, u k Indicates allocation to asset class C k The proportion of funds in b k For a length of S k A binary vector, one of whose elements is 1 and the other elements are 0, indicating which candidate portfolio obtained in the inner optimization task is selected to represent asset class C k , b ks is a binary vector b k The elements in , s is the number of the candidate portfolio; X k is a storage internal optimization task f l (k)S k N of Pareto solutions k ×S k The matrix S k is the number of Pareto solutions, i.e., the internal optimization task f l (k) is the number of candidate portfolios obtained; R() is the function of expected return, R(X k V k ) indicates that the inner optimization task f l (k) is the expected return of the candidate portfolio obtained; cov() is the function for calculating the covariance, cov(X k Vk ,X j V j ) is the inner optimization task f l (k) The candidate portfolio obtained and the inner optimization task f l The covariance of the expected returns of the candidate investment portfolio obtained in (j), j is the number of the asset category; combining the inner optimization task and the outer optimization task, in the generated mixed asset investment portfolio, investing in asset category C k The investment proportion of each product in is represented by u k *b k *X k ;

[0027] Furthermore, the inner optimization tasks are solved by using parallel technology and artificial bee colony algorithm based on external archives:

[0028] A1: Initialize the inner optimization task f l (1),f l (2),…,f l (M);

[0029] A2: Initialize M processes, each process P k Both come with an external storage W k ;

[0030] A3: The kth inner optimization task f l (k) Assigned to process P k ;

[0031] A4: For each inner optimization task, the artificial bee colony algorithm based on the external archive is executed in parallel to obtain several candidate investment portfolios for each asset class;

[0032] Furthermore, for each inner optimization task f l (k) Execute the artificial bee colony algorithm based on external archives to solve the problem, including:

[0033] B1: In process P k Initialize a bee population consisting of SN employed bees and SN observer bees in the memory of

[0034] B2: Randomly generate SN solutions, the zth solution is expressed as Each solution represents a candidate portfolio, x z,i is the element in the zth solution, indicating that it is assigned to N k The funding ratio of the i-th product among the products;

[0035] B3: For each solution, calculate its expected return f p (x z);

[0036] f p (x z )=x z T P k V k (11)

[0037] B4: For each solution, calculate its potential risk f r (x z );

[0038] f r (x z )=x z T P k cov(V k ,V k )x z (12)

[0039] B5: Based on the calculated expected returns and potential risks, find several Pareto non-dominated solutions among the SN solutions;

[0040] In the internal optimization task, Pareto dominance is defined as follows:

[0041] x z is Pareto dominated if and only if

[0042] Among them, x q is the qth solution;

[0043] B6: Add the obtained Pareto non-dominated solutions to the external storage W according to the rules. k middle;

[0044] In the process of solving the inner task, the solution is added to the external storage based on the following rules: if the external storage is empty, it is added directly; if the external storage is not empty, the Pareto dominance relationship between the solution to be added and the existing solutions in the external storage is determined, and the solutions dominated by Pareto will be removed; if the solution to be added is not dominated by Pareto, it is added to the external storage; if the external storage is full, and the solution to be added is not dominated by Pareto, and the solutions in the external storage are not Pareto dominated by the solution to be added, then the distance between the solutions is calculated, and the solution with the closest distance to other solutions is removed;

[0045] B7: For each generated solution x z , delegate a hired bee to develop the solution according to the development strategy, and obtain the developed solution;

[0046]

[0047] Among them, v z,i is the i-th element of the developed solution, x s' Is external storage W k A random solution in s',i For x s' The i-th element of m is a random solution developed by other hired bees and x m ≠x s' , x m,i For x m The i-th element of is a variable randomly distributed in [-1,1], and u is a variable randomly distributed in [0,1];

[0048] B8: Determine whether the developed solution Pareto dominates the original solution. If so, add the developed solution to the external storage W according to the rules. k And delegate it to the corresponding hired bee, otherwise the developed solution is discarded and the hired bee is still delegated to the original solution;

[0049] B9: For each solution to which hired bees are assigned, calculate its fitness function value;

[0050] For the zth assigned hired bee, z , its fitness function value is: Where N z It is the solution of all the solutions that have been assigned to hired bees. z The number of solutions that Pareto dominates;

[0051] B10: Each observer bee executes a roulette algorithm based on the fitness function value to select a solution from the solutions of the assigned employed bees;

[0052] B11: Determine whether the development times of the selected solution exceeds the threshold. If yes, randomly generate a new solution to replace it, otherwise, keep it unchanged.

[0053] B12: Develop the selected solution based on the development strategy given in step B7 to obtain a developed solution;

[0054] B13: Determine whether the developed solution Pareto dominates the original solution. If so, add the developed solution to the external storage W according to the rules. k , otherwise the developed solution is discarded;

[0055] B14: Determine whether the number of times the fitness function value is calculated exceeds the threshold, if so, external storage W k The solution in is the final candidate portfolio for this asset class, otherwise return to B7;

[0056] Furthermore, the outer optimization task is solved using an artificial bee colony algorithm based on external archives, and the mixed asset investment portfolio is obtained based on the obtained solution and the solution obtained from the inner optimization task:

[0057] C1: Initialize the outer optimization task f u ;

[0058] C2: Initialize external storage W u ;

[0059] C3: Initialize a bee population consisting of SN' only employed bees and SN' only observed bees in memory;

[0060] C4: Randomly generate SN' solutions, the z'th solution is expressed as u z' is a vector of length M, and u z' =u z',1 ,u z',2 ,…,u z',k ,…,x z',M ,u z',k for u z' The elements in represent the allocation to asset category C k The proportion of funds in z' is a matrix consisting of M vectors and b z' =b z',1 ,b z',2 ,…,b z',k ,…,b z',M , b z',k for b z' A vector in which one element is 1 and the other elements are 0, indicating which candidate portfolio obtained in the inner optimization task is selected to represent asset class C k ;

[0061] C5: For each solution, calculate its expected return

[0062]

[0063] C6: For each solution, calculate its potential risk

[0064]

[0065] C7: According to the calculated expected returns and potential risks, find several Pareto non-dominated solutions among the SN' solutions;

[0066] Pareto dominance is defined as follows:

[0067] is Pareto dominated if and only if

[0068] in, is the q'th solution;

[0069] C8: Add the obtained Pareto non-dominated solutions to the external storage W according to the rules. u middle;

[0070] In the process of solving the outer task, the solution is added to the external storage W according to the following rules u Middle: If the external storage is empty, add it directly; if the external storage is not empty, determine the Pareto dominance relationship between the solution you want to add and the existing solutions in the external storage, and remove the solutions dominated by Pareto. If the solution you want to add is not dominated by Pareto, add it to the external storage; if the external storage is full, and the solution you want to add is not dominated by Pareto, and the solutions in the external storage are not Pareto dominated by the solution you want to add, calculate the distance between the solutions and remove the solution with the closest distance to other solutions;

[0071] C9: For each generated solution Delegate a hired bee to develop the solution according to the development strategy and obtain the developed solution;

[0072] The development strategy is as follows:

[0073]

[0074] Among them, u z',k ' and b z',k ' is a vector of length M and a matrix of M vectors in the developed solution, W u A random solution in c',k and b c',k for The length M vectors and the matrix of M vectors in , is a random solution assigned to other hired bees, and u g',k and b g',k for The length of the vector is M and the matrix includes M vectors, α is a variable randomly distributed in [0,1], C is the number of times the fitness function value is calculated, and Limit is the maximum number of times the fitness function value is calculated;

[0075] C10: Determine whether the developed solution Pareto dominates the original solution. If so, add the developed solution to the external storage W according to the rules. u And delegate it to the corresponding hired bee, otherwise the developed solution is discarded and the hired bee is still delegated to the original solution;

[0076] C11: For each solution to which hired bees are assigned, calculate its fitness function value;

[0077] The solution of the z'th hired bee For example, the fitness function value is: Where N z' It is the solution of all the solutions assigned to hired bees. The number of solutions that Pareto dominates;

[0078] C12: Each observer bee executes a roulette algorithm based on the fitness function value to select a solution from the solutions of the assigned employed bees;

[0079] C13: Determine whether the development times of the selected solution exceeds the threshold. If yes, randomly generate a new solution to replace it, otherwise, keep it unchanged;

[0080] C14: Develop the selected solution based on the development strategy given in step C9 to obtain a developed solution;

[0081] C15: Determine whether the developed solution Pareto dominates the original solution. If so, add the developed solution to the external storage W according to the rules. u , otherwise the developed solution is discarded;

[0082] C16: Determine whether the number of times the fitness function value is calculated exceeds the threshold, if so, return to the external storage W u Otherwise, return to C9;

[0083] C17: According to external storage W u The solution and external storage W k The solution in generates a mixed asset portfolio;

[0084] Invest in asset class C in a mixed asset portfolio k The funding ratio of each product is

[0085] The beneficial effects of adopting the above technical solution are:

[0086] The present invention provides a non-indexed mixed asset investment portfolio optimization system, which handles the heterogeneity between asset categories and generates a better and more practical mixed asset investment portfolio without introducing an external index, thereby helping investors to make profits by constructing a mixed asset investment portfolio.

[0087] At the same time, the proposed improved artificial bee colony algorithm is used to solve the mixed asset investment portfolio. By introducing external storage and improving the solution mining strategy in the bee colony algorithm, the solution efficiency and the discreteness of the mixed asset investment portfolio are improved, thereby ensuring that the optimal mixed asset investment portfolio can be generated efficiently. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Figure 1 It is a framework diagram of a non-index mixed asset investment portfolio optimization system in an embodiment of the present invention. DETAILED DESCRIPTION

[0089] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0090] The input of the present invention is the historical market data of available products in M ​​asset categories; the output is a set of mixed asset investment portfolio optimization; the main process of this method is to formalize the mixed investment portfolio optimization problem into a two-level multi-objective optimization problem, and then use the improved artificial bee colony algorithm to solve this problem. In the formalized problem, the lower optimization task includes M optimization problems, each of which represents an asset category, and aims to build an investment portfolio with available products of the corresponding category, and the constructed investment portfolio will serve as the input of the upper optimization task. The outer optimization task is a multi-objective optimization problem, which aims to screen suitable combinations to represent asset categories and obtain the allocation of funds among M asset categories. In the improved artificial bee colony algorithm, M bee populations are first generated to solve the inner optimization task through a parallel structure. Each inner optimization task is assigned to a population, and then solved by the artificial bee colony algorithm based on the external archive. In the iteration of the artificial bee colony algorithm based on the external archive, the developed solution will be stored in the external archive in consideration of optimality and distance from other solutions. Furthermore, the outer optimization task is assigned to an artificial bee colony algorithm with an improved solution discovery strategy, which simultaneously supports the selection of representative portfolios and the allocation of funds among asset classes.

[0091] A non-indexed mixed asset portfolio optimization system, such as Figure 1 As shown, it includes a data acquisition module, a data processing module, a problem construction module and a problem solving module;

[0092] The data acquisition module is used to acquire the historical market data of the pre-assembled products as input to the data processing module; the products include stock products, fund products, bond products and financial products;

[0093] For stock products, their historical market data include the highest price, lowest price, opening price and closing price of the stock products every day within a period of time; for fund products, their historical market data include the highest price, lowest price, opening price and closing price of the fund products every day within a period of time; for bond products, their historical market data include the expected rate of return at the time of issuance; for financial products, their historical market data include the expected rate of return in the historical earnings reports they have released;

[0094] The data processing module is used to pre-process the historical market data of the pre-combined products, and classify the pre-processed historical market data of the pre-combined products according to asset categories, and obtain the historical market data of each asset category as the input of the problem construction module; the historical market data of each asset category includes the expected rate of return of different products belonging to the asset category; the asset categories include: stocks, funds, bonds and financial products;

[0095] The preprocessing is: deleting or replacing abnormal values ​​in the historical market data of stock products and fund products, filling in missing values, and then calculating the expected rate of return of stock products and fund products based on the opening price and closing price;

[0096] The problem construction module constructs a two-layer multi-objective optimization problem based on the historical market data of each asset class;

[0097] The two-layer multi-objective optimization problem includes an outer optimization task and several inner optimization tasks, each inner optimization task is used to obtain multiple candidate investment portfolios in an asset class, these candidate investment portfolios are Pareto optimal in terms of rate of return and risk, and each candidate investment portfolio includes the proportion of funds allocated to each product in the asset class; the outer optimization task is used to select an investment portfolio from the multiple candidate investment portfolios of each asset class, and allocate funds to the asset class corresponding to each selected investment portfolio; the number of the inner optimization tasks is equal to the number of asset classes;

[0098] The inner optimization task f l (k) is expressed as:

[0099] max x T P k V k (1)

[0100] min x T P k cov(V k ,V k )x (2)

[0101]

[0102] Where x is a number with a length of N. k A vector representing the allocation to asset class C k Medium k The funding ratio of each product, x i is the element in vector x, indicating the distribution to N k The proportion of funds of the i-th product among the products, i is the product number, k is the asset category number and M is the number of asset classes, C k is the kth asset class, N k For asset class C k The number of products in k Is a diagonal matrix used to represent the investor's preferences. k If the element If it is 1, it means that the investor considers N k The i-th product among the products is included in the investment portfolio, and 0 is the opposite; V k For a saved asset class C k The matrix of historical market data of all products in , cov() is the covariance function, cov(V k ,V k ) indicates V k Its own covariance; Equation 1 aims to maximize the expected return of building an investment portfolio, Equation 2 aims to minimize potential risks, Equation 3 indicates that short selling is not considered in the method proposed by the present invention, and Equation 4 indicates that the sum of the capital ratios of each product must be 1;

[0103] The outer optimization task is expressed as:

[0104]

[0105] u k ≥0,k=1,2,…,M (8)

[0106]

[0107] Among them, u k Indicates allocation to asset class C k The proportion of funds in b k For a length of S k A binary vector, one of whose elements is 1 and the other elements are 0, indicating which candidate portfolio obtained in the inner optimization task is selected to represent asset class C k , b ks is a binary vector b k The elements in , s is the number of the candidate portfolio; X k is a storage internal optimization task f l (k)Sk N of Pareto solutions k ×S k The matrix S k is the number of Pareto solutions, i.e., the internal optimization task f l (k) is the number of candidate portfolios obtained; R() is the function of expected return, R(X k V k ) indicates that the inner optimization task f l (k) is the expected return of the candidate portfolio obtained; cov() is the function for calculating the covariance, cov(X k V k ,X j V j ) is the inner optimization task f l (k) The candidate portfolio obtained and the inner optimization task f l The covariance of the expected returns of the candidate investment portfolio obtained in (j), j is the number of the asset category; combining the inner optimization task and the outer optimization task, in the generated mixed asset investment portfolio, investing in asset category C k The investment proportion of each product in is represented by u k *b k *X k ;

[0108] Equation 5 aims to maximize the expected return of a mixed asset portfolio by optimizing the allocation of funds among M asset classes. It is necessary to further explain that, as shown in Equations 9 and 10, only one portfolio is selected to represent the asset class. The main reason for this design is that portfolio optimization is considered to be a convex multi-objective optimization problem, which means that the linear combination of multiple solutions does not have Pareto optimality. Formula 6 aims to minimize potential risks. Formula 7 indicates that the sum of the asset allocation ratios must be 1. Formula 8 indicates that short selling is not considered in the method proposed in the present invention.

[0109] The problem solving module is used to solve the constructed outer optimization task and several inner optimization tasks to obtain a mixed asset investment portfolio; the mixed asset investment portfolio includes the proportion of funds allocated to each asset category and the proportion of funds allocated to each product in each asset category;

[0110] Specifically, the inner optimization task is solved by using parallel technology and an artificial bee colony algorithm based on external archives:

[0111] A1: Initialize the inner optimization task f l (1),f l (2),…,f l (M);

[0112] A2: Initialize M processes, each process P k Both come with an external storage W k ;

[0113] A3: The kth inner optimization task f l (k) Assigned to process P k ;

[0114] A4: For each inner optimization task, the artificial bee colony algorithm based on the external archive is executed in parallel to obtain several candidate investment portfolios for each asset class;

[0115] For each inner optimization task f l (k) Execute the artificial bee colony algorithm based on external archives to solve the problem, including:

[0116] B1: In process P k Initialize a bee population consisting of SN employed bees and SN observer bees in the memory of

[0117] B2: Randomly generate SN solutions, the zth solution is expressed as Each solution represents a candidate portfolio, x z,i is the element in the zth solution, indicating that it is assigned to N k The funding ratio of the i-th product among the products;

[0118] B3: For each solution Calculate its expected return f p (x z );

[0119] f p (x z )=x z T P k V k (11)

[0120] B4: For each solution Calculate its potential risk r (x z );

[0121] f r (x z )=x z T P k cov(V k ,V k )x z (12)

[0122] B5: Based on the calculated expected returns and potential risks, find several Pareto non-dominated solutions among the SN solutions;

[0123] In the internal optimization task, Pareto dominance is defined as follows:

[0124] x z is Pareto dominated if and only if

[0125] Among them, x q is the qth solution;

[0126] B6: Add the obtained Pareto non-dominated solutions to the external storage W according to the rules. k middle;

[0127] In the process of solving the inner task, the solution is added to the external storage based on the following rules: if the external storage is empty, it is added directly; if the external storage is not empty, the Pareto dominance relationship between the solution to be added and the existing solutions in the external storage is determined, and the solutions dominated by Pareto will be removed; if the solution to be added is not dominated by Pareto, it is added to the external storage; if the external storage is full, and the solution to be added is not dominated by Pareto, and the solutions in the external storage are not Pareto dominated by the solution to be added, then the distance between the solutions is calculated, and the solution with the closest distance to other solutions is removed;

[0128] B7: For each generated solution x z , delegate a hired bee to develop the solution according to the development strategy, and obtain the developed solution;

[0129]

[0130] Among them, v z,i is the i-th element of the developed solution, x s' Is external storage W k A random solution in s',i For x s' The i-th element of m is a random solution developed by other hired bees and x m ≠x s' , x m,i For x m The i-th element of is a variable randomly distributed in [-1,1], and u is a variable randomly distributed in [0,1];

[0131] B8: Determine whether the developed solution Pareto dominates the original solution. If so, add the developed solution to the external storage W according to the rules. k And delegate it to the corresponding hired bee, otherwise the developed solution is discarded and the hired bee is still delegated to the original solution;

[0132] B9: For each solution to which hired bees are assigned, calculate its fitness function value;

[0133] The solution of the zth hired bee For example, the fitness function value is: Where N z It is the solution of all the solutions that have been assigned to hired bees. z The number of solutions that Pareto dominates;

[0134] B10: Each observer bee executes a roulette algorithm based on the fitness function value to select a solution from the solutions of the assigned employed bees;

[0135] B11: Determine whether the development times of the selected solution exceeds the threshold. If yes, randomly generate a new solution to replace it, otherwise, keep it unchanged.

[0136] B12: Develop the selected solution based on the development strategy given in step B7 to obtain a developed solution;

[0137] B13: Determine whether the developed solution Pareto dominates the original solution. If so, add the developed solution to the external storage W according to the rules. k , otherwise the developed solution is discarded;

[0138] B14: Determine whether the number of times the fitness function value is calculated exceeds the threshold, if so, external storage W k The solution in is the final candidate portfolio for this asset class, otherwise return to B7;

[0139] The outer optimization task is solved by an artificial bee colony algorithm based on external archives, and the mixed asset investment portfolio is obtained based on the solution obtained and the solution obtained by the inner optimization task:

[0140] C1: Initialize the outer optimization task f u ;

[0141] C2: Initialize external storage W u ;

[0142] C3: Initialize a bee population consisting of SN' only employed bees and SN' only observed bees in memory;

[0143] C4: Randomly generate SN' solutions, the z'th solution is expressed as u z' is a vector of length M, and u z' =u z',1 ,u z',2 ,…,i z',k ,…,x z',M ,u z',k for u z'The elements in represent the allocation to asset category C k The proportion of funds in b z' is a matrix consisting of M vectors and b z' =b z',1 ,b z',2 ,…,b z',k ,…,b z',M , b z',k for b z' A vector in which one element is 1 and the other elements are 0, indicating which candidate portfolio obtained in the inner optimization task is selected to represent asset class C k ;

[0144] C5: For each solution Calculate its expected return

[0145]

[0146] C6: For each solution Calculate the potential risk

[0147]

[0148] C7: According to the calculated expected returns and potential risks, find several Pareto non-dominated solutions among the SN' solutions;

[0149] Pareto dominance is defined as follows:

[0150] is Pareto dominated if and only if

[0151] in, is the q'th solution;

[0152] C8: Add the obtained Pareto non-dominated solutions to the external storage W according to the rules. u middle;

[0153] In the process of solving the outer task, the solution is added to the external storage W according to the following rules u Middle: If the external storage is empty, add it directly; if the external storage is not empty, determine the Pareto dominance relationship between the solution you want to add and the existing solutions in the external storage, and remove the solutions dominated by Pareto. If the solution you want to add is not dominated by Pareto, add it to the external storage; if the external storage is full, and the solution you want to add is not dominated by Pareto, and the solutions in the external storage are not Pareto dominated by the solution you want to add, calculate the distance between the solutions and remove the solution with the closest distance to other solutions;

[0154] C9: For each generated solution Delegate a hired bee to develop the solution according to the development strategy and obtain the developed solution;

[0155] The development strategy is as follows:

[0156]

[0157] Among them, u z',k ' and b z',k ' is a vector of length M and a matrix of M vectors in the developed solution, W u A random solution in c',k and b c',k for The length M vectors and the matrix of M vectors in , is a random solution assigned to other hired bees, and u g',k and b g',k for The length of the vector is M and the matrix includes M vectors, α is a variable randomly distributed in [0,1], C is the number of times the fitness function value is calculated, and Limit is the maximum number of times the fitness function value is calculated;

[0158] C10: Determine whether the developed solution Pareto dominates the original solution. If so, add the developed solution to the external storage W according to the rules. u And delegate it to the corresponding hired bee, otherwise the developed solution is discarded and the hired bee is still delegated to the original solution;

[0159] C11: For each solution to which hired bees are assigned, calculate its fitness function value;

[0160] The solution of the z'th hired bee For example, the fitness function value is: Where N z' It is the solution of all the solutions assigned to hired bees. The number of solutions that Pareto dominates;

[0161] C12: Each observer bee executes a roulette algorithm based on the fitness function value to select a solution from the solutions of the assigned employed bees;

[0162] C13: Determine whether the development times of the selected solution exceeds the threshold. If yes, randomly generate a new solution to replace it, otherwise, keep it unchanged;

[0163] C14: Develop the selected solution based on the development strategy given in step C9 to obtain a developed solution;

[0164] C15: Determine whether the developed solution Pareto dominates the original solution. If so, add the developed solution to the external storage W according to the rules. u , otherwise the developed solution is discarded;

[0165] C16: Determine whether the number of times the fitness function value is calculated exceeds the threshold, if so, return to the external storage W u Otherwise, return to C9;

[0166] C17: According to external storage W u The solution and external storage W k The solution in generates a mixed asset portfolio;

[0167] Invest in asset class C in a mixed asset portfolio k The funding ratio of each product is

Claims

1. A non-indexed mixed asset portfolio optimization system, characterized in that: It includes a data acquisition module, a data processing module, a problem construction module and a problem solving module; The data acquisition module is used to acquire the historical market data of the pre-assembled products as input to the data processing module; The data processing module is used to preprocess the historical market data of the pre-combined products, and classify the pre-processed historical market data of the pre-combined products according to asset categories, and obtain the historical market data of each asset category as the input of the problem construction module, and the historical market data of each asset category includes the expected rate of return of different products belonging to the asset category; The problem construction module constructs a two-layer multi-objective optimization problem based on the historical market data of each asset class; The problem solving module is used to solve the constructed two-layer multi-objective optimization problem to obtain a mixed asset investment portfolio; the mixed asset investment portfolio includes the proportion of funds allocated to each asset category and the proportion of funds allocated to each product in each asset category.

2. A non-indexed mixed asset portfolio optimization system according to claim 1, characterized in that: The products include stock products, fund products, bond products and financial products; For stock products, their historical market data include the daily highest price, lowest price, opening price and closing price of the stock products within a time period; for fund products, their historical market data include the daily highest price, lowest price, opening price and closing price of the fund products within a time period; for bond products, their historical market data include the expected rate of return at the time of issuance; for financial products, their historical market data include the expected rate of return in the historical earnings reports they publish.

3. A non-index hybrid asset portfolio optimization system according to claim 1, characterized in that: The asset categories include: stocks, funds, bonds and financial products.

4. A non-index hybrid asset portfolio optimization system according to claim 2, characterized in that: The preprocessing is to delete or replace abnormal values ​​in the historical market data of stock products and fund products, fill in missing values, and then calculate the expected rate of return of stock products and fund products based on the opening price and closing price.

5. A non-index hybrid asset portfolio optimization system according to claim 1, characterized in that: The two-layer multi-objective optimization problem includes an outer optimization task and several inner optimization tasks, each inner optimization task is used to obtain multiple candidate investment portfolios within an asset category, these candidate investment portfolios are Pareto optimal in terms of rate of return and risk, and each candidate investment portfolio includes the proportion of funds allocated to each product in the asset category; the outer optimization task is used to select an investment portfolio from the multiple candidate investment portfolios of each asset category, and allocate funds to the asset category corresponding to each selected investment portfolio; the number of inner optimization tasks is equal to the number of asset categories.

6. A non-index hybrid asset portfolio optimization system according to claim 5, characterized in that: The inner optimization task f l (k) is expressed as: max x T P k V k (1) what time T P k (V) k ,V k )x (2) Where x is a number with a length of N. k A vector representing the allocation to asset class C k Medium k The funding ratio of each product, x i is the element in vector x, indicating the distribution to N k The proportion of funds of the i-th product among the products, i is the product number, k is the asset category number and M is the number of asset classes, C k is the kth asset class, N k For asset class C k The number of products in k Is a diagonal matrix used to represent the investor's preferences. k If the element If it is 1, it means that the investor considers N k The i-th product among the products is included in the investment portfolio, and 0 is the opposite; V k For a saved asset class C k The matrix of historical market data of all products in , cov() is the covariance function, cov(V k ,V k ) indicates V k Its own covariance.

7. A non-index hybrid asset portfolio optimization system according to claim 5, characterized in that: The outer optimization task is expressed as: u k ≥0,k=1,2,…,M (8) Among them, u k Indicates allocation to asset class C k The proportion of funds in b k For a length of S k A binary vector, one of whose elements is 1 and the other elements are 0, indicating which candidate portfolio obtained in the inner optimization task is selected to represent asset class C k , b ks is a binary vector b k The elements in , s is the number of the candidate portfolio; X k is a storage internal optimization task f l (k)S k N of Pareto solutions k ×S k The matrix S k is the number of Pareto solutions, i.e., the internal optimization task f l (k) is the number of candidate portfolios obtained; R() is the function of expected return, R(X k V k ) indicates that the inner optimization task f l (k) is the expected return of the candidate portfolio obtained; cov() is the function for calculating the covariance, cov(X k V k ,X j V j ) is the inner optimization task f l (k) The candidate portfolio obtained and the inner optimization task f l The covariance of the expected returns of the candidate investment portfolio obtained in (j), j is the number of the asset category; combining the inner optimization task and the outer optimization task, in the generated mixed asset portfolio, investing in asset category C k The investment proportion of each product in is represented by u k *b k *X k .

8. A non-index hybrid asset portfolio optimization system according to claim 6, characterized in that: The inner optimization tasks are solved by using parallel technology and artificial bee colony algorithm based on external archives: A1: Initialize the inner optimization task f l (1),f l (2),…,f l (M); A2: Initialize M processes, each process P k Both come with an external storage W k ; A3: The kth inner optimization task f l (k) Assigned to process P k ; A4: For each inner optimization task, the artificial bee colony algorithm based on external archives is executed in parallel to obtain several candidate investment portfolios for each asset class.

9. A non-index hybrid asset portfolio optimization system according to claim 8, characterized in that: For each inner optimization task f l (k) Execute the artificial bee colony algorithm based on external archives to solve the problem, including: B1: In process P k Initialize a bee population consisting of SN employed bees and SN observer bees in the memory of B2: Randomly generate SN solutions, the zth solution is expressed as Each solution represents a candidate portfolio, x z,i is the element in the zth solution, indicating that it is assigned to N k The funding ratio of the ith product among products; B3: For each solution, calculate its expected return f p (x z ); f p (x z )=x z T P k V k (11) B4: For each solution, calculate its potential risk f r (x z ); f r (x) z )=x z T P k (V) k ,V k )x z (12) B5: Based on the calculated expected returns and potential risks, find several Pareto non-dominated solutions among the SN solutions; In the internal optimization task, Pareto dominance is defined as follows: x z is Pareto dominated if and only if Among them, x q is the qth solution; B6: Add the obtained Pareto non-dominated solutions to the external storage W according to the rules. k middle; In the process of solving the inner task, the solution is added to the external storage based on the following rules: if the external storage is empty, it is added directly; if the external storage is not empty, the Pareto dominance relationship between the solution to be added and the existing solutions in the external storage is determined, and the solutions dominated by Pareto will be removed; if the solution to be added is not dominated by Pareto, it is added to the external storage; if the external storage is full, and the solution to be added is not dominated by Pareto, and the solutions in the external storage are not Pareto dominated by the solution to be added, then the distance between the solutions is calculated, and the solution with the closest distance to other solutions is removed; B7: For each generated solution x z , delegate a hired bee to develop the solution according to the development strategy, and obtain the developed solution; Among them, v z,i is the i-th element of the developed solution, x s' Is external storage W k A random solution in s',i For x s' The i-th element of m is a random solution developed by other hired bees and x m ≠x s' , x m,i For x m The i-th element of is a variable randomly distributed in [-1,1], and u is a variable randomly distributed in [0,1]; B8: Determine whether the developed solution Pareto dominates the original solution. If so, add the developed solution to the external storage W according to the rules. k And delegate it to the corresponding hired bee, otherwise the developed solution is discarded and the hired bee is still delegated to the original solution; B9: For each solution to which hired bees are assigned, calculate its fitness function value; For the zth assigned hired bee, z , its fitness function value is: Where N z It is the solution of all the solutions that have been assigned to hired bees. z The number of solutions that Pareto dominates; B10: Each observer bee executes a roulette algorithm based on the fitness function value to select a solution from the solutions of the assigned employed bees; B11: Determine whether the development times of the selected solution exceeds the threshold. If yes, randomly generate a new solution to replace it, otherwise, keep it unchanged. B12: Develop the selected solution based on the development strategy given in step B7 to obtain a developed solution; B13: Determine whether the developed solution Pareto dominates the original solution. If so, add the developed solution to the external storage W according to the rules. k , otherwise the developed solution is discarded; B14: Determine whether the number of times the fitness function value is calculated exceeds the threshold, if so, external storage W k The solution in is the final candidate portfolio for this asset class, otherwise return to B7.

10. A non-index hybrid asset portfolio optimization system according to claim 7, characterized in that: The outer optimization task is solved by an artificial bee colony algorithm based on external archives, and the mixed asset investment portfolio is obtained based on the solution obtained and the solution obtained by the inner optimization task: C1: Initialize the outer optimization task f u ; C2: Initialize external storage W u ; C3: Initialize a bee population consisting of SN' only employed bees and SN' only observed bees in memory; C4: Randomly generate SN' solutions, the z'th solution is expressed as u z' is a vector of length M, and u z' =u z',1 ,u z',2 ,…,u z',k ,…,x z',M ,u z',k for u z' The elements in represent the allocation to asset category C k The proportion of funds in b z' is a matrix consisting of M vectors and b z' =b z',1 ,b z',2 ,…,b z',k ,…,b z',M , b z',k for b z' A vector in which one element is 1 and the other elements are 0, indicating which candidate portfolio obtained in the inner optimization task is selected to represent asset class C k ; C5 : For each solution, calculate its expected return C6: For each solution, calculate its potential risk C7: According to the calculated expected returns and potential risks, find several Pareto non-dominated solutions among the SN' solutions; Pareto dominance is defined as follows: is Pareto dominated if and only if in, is the q'th solution; C8: Add the obtained Pareto non-dominated solutions to the external storage W according to the rules. u middle; In the process of solving the outer task, the solution is added to the external storage W according to the following rules u Middle: If the external storage is empty, add it directly; if the external storage is not empty, determine the Pareto dominance relationship between the solution you want to add and the existing solutions in the external storage, and remove the solutions dominated by Pareto. If the solution you want to add is not dominated by Pareto, add it to the external storage; if the external storage is full, and the solution you want to add is not dominated by Pareto, and the solutions in the external storage are not Pareto dominated by the solution you want to add, calculate the distance between the solutions and remove the solution with the closest distance to other solutions; C9: For each generated solution Delegate a hired bee to develop the solution according to the development strategy and obtain the developed solution; The development strategy is as follows: Among them, u z',k ' and b z',k ' is a vector of length M and a matrix of M vectors in the developed solution, W u A random solution in c',k and b c',k for The length M vectors and the matrix of M vectors in , is a random solution assigned to other hired bees, and u g',k and b g',k for The length of the vector is M and the matrix includes M vectors, α is a variable randomly distributed in [0,1], C is the number of times the fitness function value is calculated, and Limit is the maximum number of times the fitness function value is calculated; C10: Determine whether the developed solution Pareto dominates the original solution. If so, add the developed solution to the external storage W according to the rules. u And delegate it to the corresponding hired bee, otherwise the developed solution is discarded and the hired bee is still delegated to the original solution; C11: For each solution to which hired bees are assigned, calculate its fitness function value; The solution of the z'th hired bee For example, the fitness function value is: Where N z' It is the solution of all the solutions assigned to hired bees. The number of solutions that Pareto dominates; C12: Each observer bee executes a roulette algorithm based on the fitness function value to select a solution from the solutions of the assigned employed bees; C13: Determine whether the development times of the selected solution exceeds the threshold. If yes, randomly generate a new solution to replace it, otherwise, keep it unchanged; C14: Develop the selected solution based on the development strategy given in step C9 to obtain a developed solution; C15: Determine whether the developed solution Pareto dominates the original solution. If so, add the developed solution to the external storage W according to the rules. u , otherwise the developed solution is discarded; C16: Determine whether the number of times the fitness function value is calculated exceeds the threshold, if so, return to the external storage W u Otherwise, return to C9; C17: According to external storage W u The solution and external storage W k The solution in generates a mixed asset portfolio; Invest in asset class C in a mixed asset portfolio k The funding ratio of each product is

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