CN110852888A - Particle filter-based security investment portfolio optimization method - Google Patents

Particle filter-based security investment portfolio optimization method Download PDF

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CN110852888A
CN110852888A CN201910991928.3A CN201910991928A CN110852888A CN 110852888 A CN110852888 A CN 110852888A CN 201910991928 A CN201910991928 A CN 201910991928A CN 110852888 A CN110852888 A CN 110852888A
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黄国兴
陈林林
杨泽铭
卢为党
彭宏
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Abstract

A method for optimizing the investment combination of securities based on particle filter includes such steps as converting the solving procedure of nonlinear constraint optimization problem of investment combination of securities to the state estimation procedure of dynamic system, and iteratively searching out the investment proportional coefficient with minimum risk after investment of investment combination under the condition of expected yield by means of importance sampling, crossing and variation, weight updating, resampling and state estimation of a lot of particles. The invention introduces the crossover and mutation operations of the genetic algorithm to enrich the diversity of particles so as to improve the search range and precision. And finding out the investment proportionality coefficient which minimizes the risk after the investment of the securities portfolio under the condition of a certain expected yield by adopting a particle filtering method and an iterative search mode.

Description

Particle filter-based security investment portfolio optimization method
Technical Field
The invention relates to the field of securities investment and financial research, in particular to a securities investment portfolio optimization method based on particle filtering.
Background
The securities investment refers to the investment behavior and the investment process of investors for buying securities such as stocks, bonds, fund bonds and the like and derivatives of the securities to obtain dividends, interest and capital interest, and is an important form of direct investment. The securities portfolio refers to that an investor selects various securities as investment objects by adopting a proper method according to the risk degree and the benefit level of the securities so as to achieve the aim of minimizing the investment risk on the premise of ensuring expected income or maximizing the investment income on the premise of controlling the risk, thereby avoiding the randomness of the investment process. One of the most important principles for securities investment is the securities portfolio theory, which is proposed by the American Economizer Markowitz. He determines the basic model of the best portfolio of securities in a quantitative way. The problem of solving the optimal combination of securities is a nonlinear programming problem with multiple constraints, and a gradient-based optimization method is generally adopted in the traditional method, but the method is often not very effective in the actual solving process.
Markowtiz measures the expected profit level and the risk level of an investment by the variance of the expected profitability and profitability, respectively, and thus establishes a mean-variance model of a security portfolio. In the model built by Markowtiz, expected profitability refers to the expected value of the profitability of the portfolio of securities and expected risk refers to the variance of the profitability of the portfolio of securities.
One basic idea of the securities portfolio investment theory of Markowtiz is to determine a particular desired profitability R*. Minimizing the risk of the investment. The security portfolio optimization model at this time is shown as the following formula:
Figure BDA0002238560180000021
Figure BDA0002238560180000022
wherein n represents the number of at-risk securities to be selected by the investor; w is ai(i-1, 2, …, n) denotes the ith securityAn investment proportionality coefficient; u. ofi(i-1, 2, …, n) represents the expected profitability of the ith security; sigmai,j(i 1,2, …, n; j 1,2, …, n) represents the covariance of the ith security and the jth security; r*Representing the desired income of the investor.
At present, the modern optimization algorithm is mostly adopted for solving the security combination optimization problem, and the method mainly comprises the following steps: genetic algorithms, simulated annealing algorithms, tree algorithms, particle swarm algorithms, bee swarm algorithms, and the like. However, these methods often have some defects and shortcomings when solving the optimization problem, such as slow optimization process of genetic algorithm and easy premature convergence; although the swarm algorithm, the particle swarm algorithm and the like have strong global search capability, the local extreme points are easy to be trapped. Therefore, how to solve the security portfolio optimization problem with high efficiency and high precision is still a topic worth studying.
Disclosure of Invention
Aiming at the problem of securities investment portfolio, the invention provides a securities investment portfolio optimization method based on particle filtering. The method introduces the crossover and mutation operations of the genetic algorithm to enrich the diversity of particles so as to improve the search range and precision. And finding out the investment proportionality coefficient which minimizes the risk after the investment of the securities portfolio under the condition of a certain expected yield by adopting a particle filtering method and an iterative search mode.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a security investment portfolio optimization method based on particle filtering comprises the following steps:
converting a Markowtiz security investment portfolio optimization model into a nonlinear constraint optimization problem with an investment proportion coefficient as an independent variable and an investment risk as a fitness function, and defining a security investment expected income constraint function and an investment proportion constraint function as a formula (1) and a formula (2) respectively:
Figure BDA0002238560180000032
wherein w ═ { w ═ w1,w2,…,wn}∈R1×nRepresenting a security investment proportionality coefficient vector and having w not less than 0i≤1,(i＝1,2,…,n)，R*Is constant and represents the expected income of investors; n is an integer representing the number of at-risk securities to be selected by the investor; w is ai(i ═ 1,2, …, n) represents the investment scaling factor for the ith security; u. ofi(i-1, 2, …, n) represents the expected profitability of the ith security; then, the Markowtiz securities portfolio investment optimization model is transformed into the following nonlinear constraint optimization problem:
Figure BDA0002238560180000033
wherein σi,j(i-1, 2, …, n; j-1, 2, …, n) represents the covariance of the ith and jth securities. Thus, the Markowtiz security portfolio investment problem is converted into a nonlinear constraint optimization problem with a simple form, and the optimization fitness function is fitness (w);
and step two, describing the solving process of the non-linear constraint optimization problem of the securities investment portfolio by using a dynamic time-varying system, and modeling. The nonlinear constraint optimization problem shown in formula (3) is solved by using an iterative optimization method, and then the solving process can be regarded as a dynamic time-varying system: the iterative search times are expressed by discrete time, and the local optimal solution of each iteration is expressed by a system state value, so that the motion model of the dynamic time-varying system describes the solving process of the security portfolio nonlinear constraint optimization problem, the observation model of the dynamic time-varying system describes the updating process of the local optimal solution in the security portfolio nonlinear constraint optimization problem, and the motion model and the observation model of the system are respectively described by the following formula (4) and formula (5):
wk＝fk(wk-1,uk) (4)
zk＝fitness(wk) (5)
wherein, wk∈R1×nThe state quantity of the system at the moment K (K is 1,2, …, K) is a kind of proportional coefficient of securities investment { w }1,w2,…,wnA vector of size 1 × n is constructed; k is the total system duration; u. ofkFor the process noise of the system at time K, (K ═ 1,2, …, K), fkIs the state quantity w at time kkAnd the state quantity w at the time of k-1k-1The form of the function depends on the optimization process and convergence speed of the securities investment portfolio problem;
step three, initializing a system state, setting the total number of particles in the particle swarm to be P, and then representing the P-th (P is 1,2, …, P) particle as K (K is 1,2, …, K) time
Figure BDA0002238560180000041
Randomly initializing the initial value of each particle from the 3 rd element to the nth element as follows:
Figure BDA0002238560180000042
two other elementsAnd
Figure BDA0002238560180000044
the value of (d) is obtained by solving the following system of linear equations:
Figure BDA0002238560180000045
it is clear that,
Figure BDA0002238560180000046
initializing a state value of a system to
Figure BDA0002238560180000047
The observed value of the system is initialized to z1＝fitness(w1) The optimal solution of the system is initialized to wbest＝w1At the mostInitialization of the optimal fitness value to zbest＝z1；
Step four, importance sampling: for the P-th (P ═ 1,2, …, P) particles, according to the probability density distribution
Figure BDA0002238560180000048
Collecting new particles
Figure BDA0002238560180000049
Where K, (K ═ 1,2, …, K) represents the amount of time the system is discrete, here the probability density distribution
Figure BDA00022385601800000410
Is formed by a non-deterministic function f in the system state equationk(wk-1,uk) It is decided that the optimization process of the function should be a process with gradually reduced search range according to the system assumption, and the search is performed in a uniform distribution manner, assuming probability density distribution
Figure BDA0002238560180000051
By uniform distribution
Figure BDA0002238560180000052
To approximate, wherein ckIs a vector to be determined, and the value of the parameter should satisfy the following principle: over time, the number of iterations k increases incrementally, while vector ckThe value of each element in the vector is decreased, and the vector ckThe reduced amplitude in each iteration process directly influences the speed and the precision of the system for searching the optimal solution;
carrying out ① crossing operation, namely randomly selecting two particles, and exchanging two elements at the same position, and carrying out ② mutation operation, namely randomly selecting one particle, and randomly regenerating one element according to the combination constraint condition of securities;
step six, updating the particles to meet the securities combination optimization constraint condition, and regarding the P-th (P is 1,2, …, P) particles
Figure BDA0002238560180000053
In order to satisfy the combination constraint condition of the securities, the 1 st element and the 2 nd element are updated in the following way: first, the following system of linear equations is solved
Figure BDA0002238560180000054
Then directly order
Figure BDA0002238560180000055
Step seven, updating the global optimal solution, and sampling all the importance particles according to a fitness function fitness (-) in the system observation equation
Figure BDA0002238560180000056
Evaluating and calculating the fitness value (or observed value)
Figure BDA0002238560180000057
For any P-th, (P ═ 1,2, …, P) particles
Figure BDA00022385601800000512
All make judgments when
Figure BDA0002238560180000058
Updating the global optimal solution
Figure BDA0002238560180000059
And global optimal fitness value
Figure BDA00022385601800000510
When in
Figure BDA00022385601800000511
Global optimal solution w of the systembestAnd an optimal fitness value zbestKeeping the same;
step eight, updating the weight of the particles, firstly, calculating the weight of the effective particles, if the fitness value of the particles(or observed value)
Figure BDA0002238560180000061
Fitness value fitness (w) to the current state value of the systemk) Is large, i.e.
Figure BDA0002238560180000062
The weight of the particle is set to zero, i.e.
Figure BDA0002238560180000063
If the fitness value (or observation value) of the particle
Figure BDA0002238560180000064
Fitness value fitness (w) less than or equal to the current state value of the systemk) I.e. byThen, the euclidean distance between the fitness value (or observed value) of the particle and the current state value of the system is measured, and a smaller weight is given to the particle with a smaller euclidean distance, and a larger weight is given to the particle with a larger euclidean distance, and the implementation is as follows: when the number of particles is sufficiently large, the fitness value (or observed value) of the particles generally follows a normal distribution
Figure BDA0002238560180000066
Wherein S2For the sample variance, the weight of each particle can be calculated according to the following equation (8) and equation (9).
Figure BDA0002238560180000067
Figure BDA0002238560180000068
Obtaining the weight of all P particles
Figure BDA0002238560180000069
After that, it is subjected to a normalization process, i.e. according toFormula (10) normalizes the weight:
Figure BDA00022385601800000610
step nine, resampling particles, firstly, setting a particle shortage judgment threshold value NthTaking NthAssuming that the number of effective particles is 2P/3 or more, the number of particles is determined to be sufficient when the number of effective particles is equal to or more than 2/3, and the number of effective particles is calculated as follows:
Figure BDA0002238560180000071
if N is presenteff＜NthIf so, starting a particle resampling process, and resampling in a roulette mode; if N is presenteff≥NthThen the particle resampling process is not needed;
step ten, updating the system state, and expressing the state quantity of the system at the current time K, (K is 1,2, …, K) as a weighted average of each particle, namely:
Figure BDA0002238560180000072
step eleven, judging an iteration termination condition, outputting an optimal solution, and returning to the step four if the iteration times are not met, namely the current iteration time K is less than K, and sampling the particle importance; when the iteration number is satisfied, namely the current iteration number K is equal to K, the particle filtering process is ended, and the optimal solution w of the system is outputbestAnd its corresponding fitness value zbestSo far, the optimization problem of the securities investment portfolio is solved, and the investment proportionality coefficient with the minimum risk after the securities portfolio investment is the wbest。
The invention has the following beneficial effects: the invention describes the optimization process of the security portfolio optimization problem model as a state estimation process of a dynamic time-varying system. Within the effectively defined interval, the observed values (or fitness values) of the system gradually approach toward a decreasing risk of the portfolio investment as the discrete amount of time (or number of iterations) gradually increases. Through the processes of importance sampling, crossing and variation, weight updating, resampling, state estimation and the like of a large number of particles, the investment proportion coefficient which enables the risk after the investment of the securities portfolio to be minimum is found. The method has good stability and higher solving precision in solving the optimization problem of the portfolio of securities and is an effective method.
Detailed Description
The invention is further described below.
A security investment portfolio optimization method based on particle filtering comprises the following steps:
converting a Markowtiz security investment portfolio optimization model into a nonlinear constraint optimization problem with an investment proportion coefficient as an independent variable and an investment risk as a fitness function, and defining a security investment expected income constraint function and an investment proportion constraint function as a formula (1) and a formula (2) respectively:
Figure BDA0002238560180000081
Figure BDA0002238560180000082
wherein w ═ { w ═ w1,w2,…,wn}∈R1×nRepresenting a security investment proportionality coefficient vector and having w not less than 0i1 ≦, (i ═ 1,2, …, n), other parameters defined as follows: r*Is constant and represents the expected income of investors; n is an integer representing the number of at-risk securities to be selected by the investor;
wi(i ═ 1,2, …, n) represents the investment scaling factor for the ith security; u. ofi(i ═ 1,2, …, n) represents the expected profitability of the ith security, then the Markowtiz security portfolio investment optimization model translates into the following nonlinear constraint optimization problem:
Figure BDA0002238560180000083
wherein σi,j(i 1,2, …, n; j 1,2, …, n) represents the covariance of the ith and jth securities, so that the Markowtiz security portfolio investment problem is transformed into a simple form of nonlinear constrained optimization problem with an optimization fitness function of fitness (w);
step two, describing the solving process of the non-linear constraint optimization problem of the securities investment portfolio by using a dynamic time-varying system, modeling, and solving the non-linear constraint optimization problem shown in a formula (3) by adopting an iterative optimization mode, so that the solving process can be regarded as a dynamic time-varying system: the iterative search times are expressed by discrete time, and the local optimal solution of each iteration is expressed by a system state value, so that the motion model of the dynamic time-varying system describes the solving process of the security portfolio nonlinear constraint optimization problem, the observation model of the dynamic time-varying system describes the updating process of the local optimal solution in the security portfolio nonlinear constraint optimization problem, and the motion model and the observation model of the system are respectively described by the following formula (4) and formula (5).
wk＝fk(wk-1,uk) (4)
zk＝fitness(wk) (5)
Wherein, wk∈R1×nThe state quantity of the system at the moment K (K is 1,2, …, K) is a kind of proportional coefficient of securities investment { w }1,w2,…,wnA vector of size 1 × n is constructed; k is the total system duration; u. ofkFor the process noise of the system at time K, (K ═ 1,2, …, K), fkIs the state quantity w at time kkAnd the state quantity w at the time of k-1k-1The form of the function depends on the optimization process and convergence speed of the securities investment portfolio problem;
and step three, initializing the system state. Assuming that the total number of particles in the particle group is P, the P-th (P-1, 2, …, P) particle is represented as K at the time (K-1, 2, …, K)
Figure BDA0002238560180000091
Randomly initializing the initial value of each particle from the 3 rd element to the nth element as follows:
Figure BDA0002238560180000092
two other elements
Figure BDA0002238560180000093
And
Figure BDA0002238560180000094
the value of (d) is obtained by solving the following system of linear equations:
Figure BDA0002238560180000095
it is clear that,
Figure BDA0002238560180000096
initializing a state value of a system to
Figure BDA0002238560180000097
The observed value of the system is initialized to z1＝fitness(w1) The optimal solution of the system is initialized to wbest＝w1The optimum fitness value is initialized to zbest＝z1；
Step four, importance sampling: for the P-th (P ═ 1,2, …, P) particles, according to the probability density distribution
Figure BDA0002238560180000098
Collecting new particles
Figure BDA0002238560180000099
Where K, (K ═ 1,2, …, K) represents the amount of time the system is discrete, here the probability density distribution
Figure BDA0002238560180000101
Is formed by a non-deterministic function f in the system state equationk(wk-1,uk) It is decided that the optimization process of the function should be a process with gradually reduced search range according to the system assumption, and the search is performed in a uniform distribution manner, assuming probability density distribution
Figure BDA0002238560180000102
By uniform distribution
Figure BDA0002238560180000103
To approximate, wherein ckIs a vector to be determined, and the value of the parameter should satisfy the following principle: over time, the number of iterations k increases incrementally, while vector ckThe value of each element in the vector is decreased, and the vector ckThe reduced amplitude in each iteration process directly influences the speed and the precision of the system for searching the optimal solution;
① crossing operation, namely randomly selecting two particles, exchanging two elements at the same position, ② mutation operation, namely randomly selecting one particle, and randomly regenerating one element according to the combination constraint condition of securities;
step six, updating the particles to meet the securities combination optimization constraint condition, and regarding the P-th (P is 1,2, …, P) particles
Figure BDA0002238560180000104
In order to satisfy the combination constraint condition of the securities, the 1 st element and the 2 nd element are updated in the following way: first, the following system of linear equations is solved
Figure BDA0002238560180000105
Then directly order
Figure BDA0002238560180000106
In the seventh step,updating the global optimal solution, and sampling all the importance particles according to a fitness function fitness (-) in a system observation equationEvaluating and calculating the fitness value (or observed value)
Figure BDA0002238560180000108
For any P-th, (P ═ 1,2, …, P) particles
Figure BDA0002238560180000111
All make judgments when
Figure BDA0002238560180000112
Updating the global optimal solutionAnd global optimal fitness value
Figure BDA0002238560180000114
When in
Figure BDA0002238560180000115
Global optimal solution w of the systembestAnd an optimal fitness value zbestKeeping the same;
step eight, updating the weight of the particles, firstly, calculating the weight of the effective particles, if the fitness value (or observed value) of the particles
Figure BDA0002238560180000116
Fitness value fitness (w) to the current state value of the systemk) Is large, i.e.
Figure BDA0002238560180000117
The weight of the particle is set to zero, i.e.
Figure BDA0002238560180000118
If the fitness value (or observation value) of the particle
Figure BDA0002238560180000119
Fitness value fitness (w) less than or equal to the current state value of the systemk) I.e. by
Figure BDA00022385601800001110
Then, the euclidean distance between the fitness value (or observed value) of the particle and the current state value of the system is measured, and a smaller weight is given to the particle with a smaller euclidean distance, and a larger weight is given to the particle with a larger euclidean distance, and the implementation is as follows: when the number of particles is sufficiently large, the fitness value (or observed value) of the particles generally follows a normal distributionWherein S2From this, the weight of each particle is calculated according to the following equations (8) and (9):
Figure BDA00022385601800001113
obtaining the weight of all P particles
Figure BDA00022385601800001114
Then, normalization processing is performed on the weight values, that is, the weight values are normalized according to the following formula (10):
Figure BDA00022385601800001115
step nine, resampling particles, wherein in order to reduce the influence of particle shortage on system convergence, a particle resampling process needs to be started, and firstly, a particle shortage judgment threshold value N is setthTaking NthAssuming that the number of effective particles is 2P/3 or more, the number of particles is determined to be sufficient when the number of effective particles is equal to or more than 2/3, and the number of effective particles is calculated as follows:
if N is presenteff＜NthIf so, starting a particle resampling process, and resampling in a roulette mode; if N is presenteff≥NthThen the particle resampling process is not needed;
step ten, updating the system state. At present, the state quantity of the system at time K (K ═ 1,2, …, K) is expressed as a weighted average of the particles, i.e.:
Figure BDA0002238560180000122
step eleven, judging an iteration termination condition, outputting an optimal solution, and returning to the step four if the iteration times are not met, namely the current iteration time K is less than K, and sampling the particle importance; when the iteration number is satisfied, namely the current iteration number K is equal to K, the particle filtering process is ended, and the optimal solution w of the system is outputbestAnd its corresponding fitness value zbestSo far, the optimization problem of the securities investment portfolio is solved, and the investment proportionality coefficient with the minimum risk after the securities portfolio investment is the wbest。
And (3) experimental comparison: to verify the performance of the method of the present invention for solving the portfolio optimization problem of securities, the following two typical examples were used for testing.
Example 1: assuming that the portfolio consists of 3 securities, the expected securities investment profitability is 6.8%, and the profitability covariance thereof are shown in table 1. The minimum risk investment proportion coefficient vector of the security combination obtained by the method of the invention is as follows: w ═ 0.60916817456292, 0.19805907398015, 0.19277275145693. The results of the calculations for the various algorithms are shown in table 2.
Figure BDA0002238560180000123
Figure BDA0002238560180000131
TABLE 1
Figure BDA0002238560180000132
TABLE 2
Example 2: assuming that the portfolio consists of 6 securities, the return on investment is 20.5%, and the return and the covariance of return are shown in Table 3. The minimum risk investment proportion coefficient vector of the security combination obtained by the method of the invention is as follows: w ═ [0.07459492705459, 0.00000000001454, 0.16811832788656, 0.24520471325523, 0.29758477229673, 0.21449725949235 ]. The results of the calculations for the various algorithms are shown in table 4.
TABLE 3
Figure BDA0002238560180000134
TABLE 4
From these calculations it can be seen that: the method of the invention has better result than other algorithms in the optimization process of solving the securities investment portfolio, and the algorithm also shows higher optimizing precision and stronger optimizing performance.

Claims (4)

1. A method for optimizing a security portfolio based on particle filtering is characterized by comprising the following steps:
converting a Markowtiz security investment portfolio optimization model into a nonlinear constraint optimization problem with an investment proportion coefficient as an independent variable and an investment risk as a fitness function, and defining a security investment expected income constraint function and an investment proportion constraint function as a formula (1) and a formula (2) respectively:
Figure FDA0002238560170000011
Figure FDA0002238560170000012
wherein w ═ { w ═ w1,w2,…,wn}∈R1×nRepresenting a security investment proportionality coefficient vector and having w not less than 0i≤1,(i＝1,2,…,n)，R*Is constant and represents the expected income of investors; n is an integer representing the number of at-risk securities to be selected by the investor; w is ai(i ═ 1,2, …, n) represents the investment scaling factor for the ith security; u. ofi(i ═ 1,2, …, n) represents the expected profitability of the ith security, then the Markowtiz security portfolio investment optimization model translates into the following nonlinear constraint optimization problem:
wherein σi,j(i 1,2, …, n; j 1,2, …, n) represents the covariance of the ith and jth securities, so that the Markowtiz security portfolio investment problem is transformed into a simple form of nonlinear constrained optimization problem with an optimization fitness function of fitness (w);
step two, describing the solving process of the non-linear constraint optimization problem of the securities investment portfolio by using a dynamic time-varying system, modeling, and solving the non-linear constraint optimization problem shown in a formula (3) by adopting an iterative optimization mode, so that the solving process can be regarded as a dynamic time-varying system: the iterative search times are expressed by discrete time, and the local optimal solution of each iteration is expressed by a system state value, so that the motion model of the dynamic time-varying system describes the solving process of the security portfolio nonlinear constraint optimization problem, the observation model of the dynamic time-varying system describes the updating process of the local optimal solution in the security portfolio nonlinear constraint optimization problem, and the motion model and the observation model of the system are respectively described by the following formula (4) and formula (5):
wk＝fk(wk-1,uk) (4)
zk＝fitness(wk) (5)
wherein, wk∈R1×nThe state quantity of the system at the moment K (K is 1,2, …, K) is a kind of proportional coefficient of securities investment { w }1,w2,…,wnA vector of size 1 × n is constructed; k is the total system duration; u. ofkFor the process noise of the system at time K, (K ═ 1,2, …, K), fkIs the state quantity w at time kkAnd the state quantity w at the time of k-1k-1The form of the function depends on the optimization process and convergence speed of the securities investment portfolio problem;
step three, initializing the system state, and setting the total number of particles in the particle swarm to be P, then the (P ═ 1,2, …, P) particles at time K, (K ═ 1,2, …, K) can be represented as
Figure FDA0002238560170000021
Initializing a state value of a system to
Figure FDA0002238560170000022
The observed value of the system is initialized to z1＝fitness(w1) The optimal solution of the system is initialized to wbest＝w1The optimum fitness value is initialized to zbest＝z1；
Step four, importance sampling: for the P-th (P ═ 1,2, …, P) particles, according to the probability density distribution
Figure FDA0002238560170000023
Collecting new particles
Figure FDA0002238560170000024
Where K, (K ═ 1,2, …, K) represents the amount of time the system is discrete, here the probability density distributionIs formed by a non-deterministic function in the system state equationfk(wk-1,uk) Determining that the optimization process of the function is a process that the search range is gradually reduced according to the system assumption, and searching in a uniformly distributed mode;
① crossing operation, namely randomly selecting two particles, exchanging two elements at the same position, ② mutation operation, namely randomly selecting one particle, and randomly regenerating one element according to the combination constraint condition of securities;
step six, updating the particles to meet the securities combination optimization constraint condition;
step seven, updating the global optimal solution, and sampling all the importance particles according to a fitness function fitness (-) in the system observation equationEvaluating and calculating the fitness valueFor any P-th, (P ═ 1,2, …, P) particles
Figure FDA0002238560170000028
All make judgments when
Figure FDA0002238560170000029
Updating the global optimal solution
Figure FDA00022385601700000210
And global optimal fitness value
Figure FDA00022385601700000211
When in
Figure FDA00022385601700000212
Global optimal solution w of the systembestAnd an optimal fitness value zbestKeeping the same;
step eight, updating the weight of the particles, firstly, calculating the weight of the effective particles, if the fitness value of the particles
Figure FDA00022385601700000213
Fitness value fitness (w) to the current state value of the systemk) Is large, i.e.
Figure FDA00022385601700000214
The weight of the particle is set to zero, i.e.
Figure FDA00022385601700000215
If the fitness value of the particle
Figure FDA00022385601700000216
Fitness value fitness (w) less than or equal to the current state value of the systemk) I.e. by
Figure FDA00022385601700000217
Then, the euclidean distance between the fitness value of the particle and the current state value of the system is measured, a smaller weight is given to the particle with a smaller euclidean distance, and a larger weight is given to the particle with a larger euclidean distance, and the implementation manner is as follows: when the number of particles is sufficiently large, the fitness value of the particles follows a normal distribution
Figure FDA0002238560170000031
Wherein S2From this, the weight of each particle is calculated according to the following equations (8) and (9):
Figure FDA0002238560170000032
Figure FDA0002238560170000033
obtaining the weight of all P particles
Figure FDA0002238560170000034
Then, normalization processing is performed on the weight values, that is, the weight values are normalized according to the following formula (10):
Figure FDA0002238560170000035
step nine, resampling particles, firstly, setting a particle shortage judgment threshold value NthTaking NthAssuming that the number of effective particles is 2P/3 or more, the number of particles is determined to be sufficient when the number of effective particles is equal to or more than 2/3, and the number of effective particles is calculated as follows:
Figure FDA0002238560170000036
if N is presenteff＜NthIf so, starting a particle resampling process, and resampling in a roulette mode; if N is presenteff≥NthThen the particle resampling process is not needed;
step ten, updating the system state, and expressing the state quantity of the system at the current time K, (K is 1,2, …, K) as a weighted average of each particle, namely:
Figure FDA0002238560170000037
step eleven, judging an iteration termination condition, outputting an optimal solution, and returning to the step four if the iteration times are not met, namely the current iteration time K is less than K, and sampling the particle importance; when the iteration number is satisfied, namely the current iteration number K is equal to K, the particle filtering process is ended, and the optimal solution w of the system is outputbestAnd its corresponding fitness value zbestSo far, the optimization problem of the securities investment portfolio is solved, and the investment proportionality coefficient with the minimum risk after the securities portfolio investment is the wbest。
2. The method as claimed in claim 1, wherein in step three, the initialization of system state is performed by using initial values of each particle
Figure FDA0002238560170000038
The selection mode is as follows: first, the initial value of each particle from the 3 rd element to the nth element is randomly initialized to:
Figure FDA0002238560170000039
wherein rand (·) represents a random function; then, the particles
Figure FDA00022385601700000310
Two other elements of
Figure FDA00022385601700000311
And
Figure FDA00022385601700000312
the value of (d) is obtained by solving the following system of linear equations:
Figure FDA0002238560170000041
wherein the content of the first and second substances,
Figure FDA0002238560170000042
3. the method for optimizing the portfolio of securities based on particle filtering as claimed in claim 1 or 2, wherein in said step four, said probability density function
Figure FDA0002238560170000043
Should adopt even distribution
Figure FDA0002238560170000044
To approximate, wherein ckIs a vector to be determined, and the value of the parameter should satisfy the following principle: over time, the number of iterations k increases incrementally, while vector ckThe value of each element in the vector is decreased, and the vector ckThe reduced amplitude during each iteration will directly affect the speed and accuracy with which the system finds the optimal solution.
4. The method for optimizing the portfolio of securities based on particle filtering as claimed in claim 1 or 2, wherein: in the sixth step, the updating of the particles to make the particles meet the securities combination optimization constraint condition comprises the following implementation steps: for the P-th (P ═ 1,2, …, P) particles
Figure FDA0002238560170000045
In order to satisfy the constraint condition of combination of securities, the 1 st element and the 2 nd element are updated, firstly, the following linear equation system is solved
Figure FDA0002238560170000046
Then directly order
Figure FDA0002238560170000047
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114145749A (en) * 2021-11-05 2022-03-08 浙江工业大学 ECG signal limited innovation rate sampling method based on optimization model
CN115619545A (en) * 2022-05-12 2023-01-17 刘宏 Time line automatic security trading risk control system based on artificial intelligence

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105809270A (en) * 2016-01-05 2016-07-27 淮海工学院 Security investment combination evolution optimization method based on interval multi-target planning
CN106251217A (en) * 2016-04-07 2016-12-21 合肥工业大学 Portfolio Optimization method based on historical analogy method WCVaR Risk Model
CN108492189A (en) * 2018-03-22 2018-09-04 张家林 Portfolio Selection selection method, device and equipment
CN110633845A (en) * 2019-08-27 2019-12-31 江苏大学 Method for optimizing financial investment problem by using weighted preference-based pso

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105809270A (en) * 2016-01-05 2016-07-27 淮海工学院 Security investment combination evolution optimization method based on interval multi-target planning
CN106251217A (en) * 2016-04-07 2016-12-21 合肥工业大学 Portfolio Optimization method based on historical analogy method WCVaR Risk Model
CN108492189A (en) * 2018-03-22 2018-09-04 张家林 Portfolio Selection selection method, device and equipment
CN110633845A (en) * 2019-08-27 2019-12-31 江苏大学 Method for optimizing financial investment problem by using weighted preference-based pso

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114145749A (en) * 2021-11-05 2022-03-08 浙江工业大学 ECG signal limited innovation rate sampling method based on optimization model
CN114145749B (en) * 2021-11-05 2024-04-05 浙江工业大学 ECG signal limited new-information rate sampling method based on optimization model
CN115619545A (en) * 2022-05-12 2023-01-17 刘宏 Time line automatic security trading risk control system based on artificial intelligence

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