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Opposition-based Differential Evolution Algorithm And Its Application To Portfolio Problem

Posted on:2022-09-22Degree:MasterType:Thesis
Country:ChinaCandidate:Q XiongFull Text:PDF
GTID:2518306341951499Subject:Mathematics
Abstract/Summary:PDF Full Text Request
Swarm intelligence algorithm has more obvious advantages than traditional optimization algorithm for solving large-scale optimization problems,especially some NP-hard problems.However,there are also limitations,so how to improve this kind of algorithm has become the focus of the majority of scholars.Differential Evolution(DE)algorithm is a kind of swarm intelligence algorithm,which can be regarded as a simulation model of biological evolution process.Through constant iteration of mutation and crossover operation,individuals with high fitness are selected to enter the next generation.Because of its fast running speed and strong robustness,it has been widely used in many fields.This paper explains DE algorithm in detail,and also introduces the Opposition-based Differential Evolution(ODE)algorithm generated by introducing the Opposition-Based Learning(OBL)strategy into DE algorithm.Then on the basis of ODE,an Opposition-based Differential Evolution Algorithm with Neighborhood-based self-adaptive Uniform Mutation(NODE)is proposed.NODE introduces a uniform mutation operator based on the adjacent neighborhood of the site,which makes full use of the dual information of the current individual and the population,and adapts the search interval through the real-time maximum and minimum values of the current population.In addition,a multi-stage perturbation strategy is also introduced to divide the algorithm running process into three stages in an average way,and the convergence speed can be better adjusted in each stage.In order to verify the performance of the improved algorithm,10 test functions are selected to conduct comparative simulation experiments between DE,ODE and NODE.The results show that the improved algorithm proposed in this paper has better overall performance,easier to avoid "prematurity",higher convergence precision and better robustness.The essence of portfolio problem is to allocate the limited capital rationally and optimally in order to achieve the balance between income and risk.This paper introduces the general framework of the portfolio problem,and describes and proves four models in detail:mean-variance(M-V)model,mean-VaR(M-VAR)model,mean-CVaR(M-CVAR)model and high-order moment model.The effective frontier of M-V and M-VAR model is obtained by introducing the risk aversion coefficient,and the effective frontier of M-VAR model is found to be a subset of the former.The effective frontier of M-VAR model under different confidence levels is also discussed.In this paper,NODE is applied to portfolio problems to broaden its application scope in real world problems.The one-year closing data of 50 stocks in CSI 300 were randomly selected for experimental analysis.NODE is found to perform better than DE.Furthermore,the performance of M-V model and M-VAR model is further compared through the results of NODE's operation.It is found that compared with Variance,the experimental indicator VAR has a better control effect on the measurement of risk and is more suitable for risk-averse investors.Moreover,the greater the confidence level is,the better the model can control the risk.This also provides a practical problem-solving tool for the majority of investors.
Keywords/Search Tags:Differential Evolution Algorithm, Opposition-based learning, Neighborhood Mutation, Portfolio, Mean-VAR Model
PDF Full Text Request
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