Research On Portfolio Problem Considering Parameter Uncertainty And Investor’s Behavioral Characteristic

Portfolio optimization as an effective wealth allocation and risk management tool has attracted a lot attention from both academics and practitioners.The basic idea of portfolio optimization is to allocate investors’ wealth amount a number of assets so that the investment goal can be achieved under uncertain situations.However,in real investment,since the security market is a complex dynamic system,it is difficult to exactly estimate the distribution parameters of asset returns by historical data.In addition,lots of researches have shown that the mean-variance portfolio model is highly sensitive to expected returns:a small perturbation in expected returns may lead to a large variation in the optimum portfolio allocation.In the research field of parameter uncertainty,both of the fuzzy theory and the robust theory have been widely used.Therefore,this paper uses the fuzzy theory and the robust theory to handle the uncertainty problem in the portfolio model.Moreover,with the development of behavioral finance,improving portfolios’ performance by integrating investors’ behavioral characteristic has become a new research direction.The studies of behavioral finance have found that investors are bounded rationality and usually have cognitive bias.Their psychological and emotional factors play an important role in decision-making.Therefore,from the perspective of integrating the parameter uncertainty and investor’s behavioral characteristic,this paper researches the portfolio selection problem considering parameter uncertainty and investor’s behavioral characteristic,which is of great theoretical and practical significance on portfolio optimization problem.In this paper,the portfolio selection problem considering parameter uncertainty and investor’s behavioral characteristic is researched intensively.The main aspects of research work are conducted as follows:(1)Research on random fuzzy portfolio problem with different investors’ risk characteristic.Specially,as investors face the uncertainty of randomness and fuzziness simultaneously in stock market,the paper defines the security returns as random fuzzy variables.Based on the prospect theory and investors’ psychological trait,a random fuzzy portfolio model with different investors’ risk characteristic is proposed by constructing different random fuzzy returns,target weights and membership functions of expected return.Under the decline and rise stages of stock market,the differences of portfolios for investors with various risk characteristic and the performance of the proposed model are empirically studied.(2)Research on robust mean-CVaR portfolio problem from a safety criterion perspective.Specially,considering the uncertainty in real stock market,we regard the security return as an interval random variable and develop a robust mean-CVaR portfolio model based on the robust theory.Following the duality theory,the proposed model can be transformed as a linear programming problem,which reduces the computational complexity and contributes to solve a large-scale portfolio model.To consider investors’ safety requirement,a concept of the most violated probability is introduced,which can be used to adjust the conservatism of the proposed model and reflect investors’ safety requirement intuitively.The performance of the proposed model is empirically studied.(3)Research on robust portfolio problem under regime-dependent and loss aversion.Specially,from the perspective of the return and risk of financial assets vary over regimes,the loss aversion portfolio model under regime-dependent is presented,where the prospect theory is used to describe investors’ loss aversion characteristic and the transaction cost of portfolio adjustment is taken into consideration.Additionally,considering the parameter uncertainty,we regard the asset return as an interval random variable and then a robust portfolio model under regime-dependent and loss aversion is proposed.Following the duality theory,the proposed model can be transformed as a linear programming problem,which reduces the computational complexity.Moreover,to adjust the conservatism of the proposed model and reflect investors’ safety requirement intuitively,a concept of the most violated probability is introduced to determine the value of the robust parameter.Finally,the performance of the proposed model is empirically studied.(4)Research on robust multi-period portfolio problem based on prospect theory.Specially,considering investors’ behavioral factor and the uncertainty of parameters,a multi-period robust portfolio model based on prospect theory is developed.Based on the prospect theory,we propose a dynamic prospect theory value function with dynamically updated wealth reference and loss aversion parameter.Furthermore,a particle swarm optimization algorithm with an aging leader and multi-frequency vibration(ALMV-PSO)is introduced to solve the robust multi-period portfolio problem.In ALMV-PSO,we also design a two-stage initialization strategy and a PSO based stochastic ranking approach.The two-stage initialization strategy guarantees that all of the initial particles are in a feasible region and with a high level of diversity.The PSO based stochastic ranking approach automatically balances between the objective function value and the constraint violation function value for the constrained portfolio problem.Finally,we illustrate the robust model with real market data and show its effectiveness based on the performance of the proposed algorithm.At the end of the dissertation,we summarize the results and contributions of researches,and point out the limitations and further research directions in the future.