The Problem Of Portfolio Under The Cumulative Prospect Theory Analysis And Solution

Generally speaking,the expected utility theory proposed by Von Neumann and Morgenstern was often used to solve the optimal portfolio problem.However,when considering that investors will show different investment attitudes when facing profits or losses,it is impossible for anyone in real life to be completely rational.Therefore,this paper uses the Cumulative prospect theory(CPT)proposed by Kahneman and Tversky as the basic model,This model fully considers the psychological factors of investors in the investment process,and on this basis,specific utility functions,distribution functions of excess returns,and weight functions are substituted to solve the optimal investment portfolio.This paper first introduces the Cumulative prospect theory model,several important weight functions set by predecessors and some parameter values obtained from empirical research,and gives some assumptions about the utility function and weight function,as well as the limited range of parameters in the function.Secondly,in order to make the model more suitable for practical situations,this paper gives the definition of the fitness of the Cumulative prospect theory model,which is described in the following selection of utility function and distribution function The determination of parameters and the process of solving the optimal investment portfolio play a crucial role.Under the condition of satisfying the model’s well posedness,through analysis,the relationship that should be satisfied between the distribution function and the weight function under certain conditions is obtained.Finally,a cubic weight function that satisfies all assumptions was first selected,and based on this,a uniform distribution function was determined.Finally,two different utility functions were determined: exponential utility function and logarithmic utility function.Based on these two cases,the investor’s long and short positions were discussed.The solution of the exponential utility function was to solve the optimal investment portfolio solution given the limited relationship between parameters,In the case of a logarithmic utility function,the actual economic significance in the model is explained.Due to the large number of parameters and the complexity of the model,the value of one parameter is determined first,and then the range of another parameter is determined by the economic significance.Finally,the value of the parameter is obtained near the parameter value obtained from empirical analysis in previous papers to obtain the optimal investment portfolio solution for this situation;In the final case,the return on risky assets is determined as a negative exponential distribution function,thereby obtaining the distribution of excess return.The utility function is chosen as an exponential utility function,which results in a more complex marginal value function.Due to the discovery of removable breakpoints in the obtained function through calculation,the function is first completed,and then the shape of the function is discussed.Finally,reasonable parameters are confirmed to obtain the optimal investment portfolio solution.