A Mean-Variance Problem in the Constant Elasticity of Variance (CEV) Model (Communications in Mathematical Research, 2021)
In this paper, we focus on a constant elasticity of variance (CEV) modeland want to find its optimal strategies for a mean-variance problem under two constrained controls: reinsurance/new business and investment (no-shorting). First, aLagrange multiplier is introduced to simplify the mean-variance problem and thecorresponding Hamilton-Jacobi-Bellman (HJB) equation is established. Via a powertransformation technique and variable change method, the optimal strategies withthe Lagrange multiplier are obtained. Final, based on the Lagrange duality theorem,the optimal strategies and optimal value for the original problem (i.e., the efficientstrategies and efficient frontier) are derived explicitly.