Optimal Investment for a DC Pension Plan under VaR Regulations and Minimum Insurance with Inflation Risk

In this paper, we study an optimal investment problem under joint initial-time and intermediate-time Value-at-Risk regulations and a portfolio insurance (PI) constraint on terminal wealth faced by a defined-contribution pension fund manager. The objective is to maximize the expected utility from the terminal wealth exceeding the minimum guaranteed annuity by allocating assets in a risk-free bond, an indexed bond and a stock. We apply the martingale method to transform a dynamic optimization problem to a static pointwise optimization problem and derive the closed-form precommitted strategies. Our numerical results show that an intermediate-time VaR constraint can significantly change the tail distribution of the optimal terminal surplus process and greatly reduce the risk of loss for "bad" market states