Optimal Mean-Variance Portfolio With Liability Based On Discontinuous Stochastic Process And A No-Shorting Constraint

Abstract

This paper investigates an optimal mean-variance portfolio selection model. The model is formulated with a free risky asset, a risky asset and a liability under discontinuous prices which follow jump-diffusion processes. Moreover, the short-selling of stock is prohibited. The correlation between the risky asset and the liability is considered. The corresponding Hamilton-Jacobi-Bellman equation of the problem is presented. The solution of the HJB equation based on the theory of stochastic LQ control. The optimal dynamic strategy and the efficient frontier in closed forms are derived explicitly.