Behavioral mean-risk portfolio selection in continuous time via quantile

Abstract

A behavioral mean-risk portfolio selection problem in continuous time is formulated and studied in this article. Based on the standard mean-variance portfolio selection problem, the cumulative distribution function of the cash flow is distorted by a probability distortion function. This probability distortion function represents the risk preference in a different way. Then the problem is no longer a convex optimization problem. This feature distinguishes it from the conventional linear-quadratic (LQ) problems. The stochastic optimal LQ control theory no longer applies. We take the quantile function of the terminal cash flow as the decision variable. The corresponding optimal terminal cash flow can be recovered by the optimal quantile function. Then the efficient strategy is the hedging strategy of the optimal terminal cash flow.

Keywords:

• Probability distortion
• mean-risk
• portfolio selection
• quantile approach

MATHEMATICS SUBJECT CLASSIFICATION:

• 90C39
• 91B30
• 91G80

Additional information

Funding

The work is supported by National Natural Science Foundation of China (Grant Nos. 11871220, 11801179, 11871219, 12071224), the “Chenguang Program” supported by Shanghai Education Development Foundation and Shanghai Municipal Education Commission (No. 18CG26), and 111 Project (B14019).