Optimal investment of DC pension plan under a joint VaR-ES constraint

In this paper, we investigated an optimal investment problem of a defined contribution (DC) pension plan under a joint Value-at-Risk (VaR) and an expected shortfall (ES) constraint. By using a martingale method, we transformed a dynamic optimization problem to a static pointwise optimization problem and derived the closed-form representations of the optimal wealth and portfolio processes in terms of the state price density. Numerical results showed that in comparison to only an ES constraint or a VaR constraint, the joint VaR-ES constraint can not only improve risk management for the bad economic states but also lower the volatility of the optimal terminal wealth.