Optimal Mean-variance Investment Strategy Under Value-at-risk Constraints

This paper is devoted to study the efects arising from imposing a value-at-risk(VaR) constraint in mean-variance portfolio selection problem for an investor who re-ceives a stochastic cash flow which he/she must then invest in a continuous-time finan-cial market. For simplicity, we assume that there is only one investment opportunityavailable for the investor, a risky stock. Using techniques of stochastic linear-quadratic(LQ) control, the optimal mean-variance investment strategy with and without VaRconstraint are derived explicitly in closed forms, based on solution of correspondingHamilton-Jacobi-Bellman (HJB) equation. Furthermore, some numerical examples areproposed to show how the addition of the VaR constraint afects the optimal strategy.