Bat Algorithm For Multiobjective Fuzzy Portfolio Optimization Selection

Markowitz's mean-variance model marked a new epoch in modern portfolio theory.Traditionally,the portfolio model is always based on the probability theory,and assumed that the security returns are random variables.However,the financial markets also have some nonprobabilistic features,such as vagueness and ambiguity.Therefore,some researchers study portfolio selection on the basis of fuzzy set theory and regards return as fuzzy variable.Note that most of the researches have proposed a series of multiobjective fuzzy portfolio optimization problems,but most of them are turn the multiobjective problem into single-objective portfolio problem,few researches directly use intelligent algorithm to solve multiobjective portfolio optimization problem.Thus,the purpose of this thesis is to study multiobjective portfolio selection problems on the basis of fuzzy set theory and intelligent algorithm theory.(1)We propose a multiobjective mean-semivariance-entropy model with realistic constraints based on possibilistic theory,and design a hybrid BA-DE to solve the model.Firstly,A multiobjective mean–semivariance–entropy model based on possibilistic theory is proposed for portfolio selection.Specifically,it simultaneously optimizes the return,risk and portfolio diversification,taking into account transaction costs,liquidity,buy-in thresholds,and cardinality constraints.After that,a new metaheuristic method termed as the hybrid BA–DE is developed by combining features of the bat algorithm(BA)and differential evolution(DE).Finally,a numerical example is given to demonstrate the effectiveness of the proposed model and algorithm.(2)We propose a multiperiod multiobjective mean-Va R model based on credibility theory,and design an improved multiobjective bat algorithm to solve the model.Firstly,under the framework of mean-variance,we substitute variance by Va R as risk measure and propose a multiperiod multiobjective mean–Va R model based on credibility theory.Then,to solve the proposed model efficiently,an improved multiobjective bat algorithm termed IMBA is designed,in which three new strategies,i.e.,the global best solution selection strategy,candidate solution generation strategy,and competitive learning strategy,are proposed to increase the convergence speed and improve the solution quality.Finally,a numerical example is given to demonstrate the effectiveness of the proposed model and algorithm.