The Optimal Solution under Cumulative Prospect Theory

Abstract

[[abstract]]A fundamental problem in the financial mathematics is to find out an optimal strategy for the investment. And the most used setting to discuss the optimal investment is the expected utility optimization. But we find that there are some shortages in expected utility theory. In order to overcome these shortages, we use the cumulative prospect theory to replace the expected utility theory. In this thesis, we make a connection between the expected utility theory and the cumulative prospect theory. And we consider an optimal problem for a discrete type under the cumulative prospect theor