Behavioral mean-variance portfolio selection

In this paper, a behavioral mean-variance portfolio selection problem in continuous time is formulated and studied. Unlike in the standard mean-variance portfolio selection problem, the cumulative distribution function of the cash flow is distorted by the probability distortion function used in the behavioral mean-variance portfolio selection problem. With the presence of distortion functions, the convexity of the optimization problem is ruined, and the problem is no longer a conventional linear-quadratic (LQ) problem, and we cannot apply conventional optimization tools like convex optimization and dynamic programming. To address this challenge, we propose and demonstrate a solution scheme by taking the quantile function of the terminal cash flow as the decision variable, and then replace the corresponding optimal terminal cash flow with the optimal quantile function. This allows the efficient frontier and the efficient strategy to be exploited.