Optimal Portfolio Selection For Behavioral Investor In Incomplete Market

In this paper,we mainly study the optimal portfolio selection of investors based on the cumulative prospect theory under the condition of incomplete market.The optimal portfolio selection problem is one of the most important issues in the field of financial economics,especially in the field of asset pricing.It mainly studies the optimal decision made by investors who can make flexible adjustment to the changing price of the underlying asset.It reflects the dynamic behavior of asset prices,the investment decision-making process and the characteristics of the investors in the stock market.Compared with the previous research on portfolio selection problem of the literature,this paper uses the incomplete market and the cumulative prospect theory(including reference point,loss aversion and probability distortion)as the breakthrough point,analyzes optimal investment decision of behavior investors.The market conditions,utility of investors and other hypotheses are closer to reality,especially the reality of our country,rather than the traditional theory that requires strict market assumptions,and completely eliminates emotional behavior of human factors,to pursue investment decision under the condition of perfect theory.Because of the incompleteness of market,we should reduce the dimension of the Brown movement to make it equal to the number of assets,this will also make the price nuclear and martingale measure change;probability distortion and other factors will also make the traditional stochastic control theory invalid,introduction of split and Choquet minimization method make the solution of negative problem more complicated.In complete market,we get only two kinds of situations,while in incomplete market,there would be three.This paper presents the optimal portfolio selection of investors based on the cumulative prospect theory under the condition of incomplete market.The final analytical solution and numerical simulation are obtained to provide investors with more realistic reference for investment decision-making.