Precommitted Strategies with Initial-Time and Intermediate-Time Value-at-Risk Constraints

This paper considers the expected utility portfolio optimization problem with initial-time and intermediate-time Value-at-Risk constraints on terminal wealth. We derive the closed-form solutions which are optimal among all feasible controls at initial time, i.e., precommitted strategies. Moreover, the precommitted strategies are also optimal at the intermediate time for “bad” market states. A contingent claim on Merton’s portfolio is constructed to replicate the optimal portfolio. We find that risk management with intermediate-time risk constraints is prudent in hedging “bad” intermediate market states and performs significantly better than the one terminal-wealth risk constraint solutions under the relative loss ratio measure.