A Mean-Variance Problem in the Constant Elasticity of Variance (CEV) Model

Abstract

In this paper, we focus on a constant elasticity of variance (CEV) model and want to find its optimal strategies for a mean-variance problem under two constrained controls: reinsurance/new business and investment (no-shorting). First, a Lagrange multiplier is introduced to simplify the mean-variance problem and the corresponding Hamilton-Jacobi-Bellman (HJB) equation is established. Via a power transformation technique and variable change method, the optimal strategies with the Lagrange multiplier are obtained. Final, based on the Lagrange duality theorem, the optimal strategies and optimal value for the original problem (i.e., the efficient strategies and efficient frontier) are derived explicitly.