A maximum principle for a stochastic control problem with multiple random terminal times

Abstract

In the present paper we derive, via a backward induction technique, an ad hoc maximum principle for an optimal control problem with multiple random terminal times. We thus apply the aforementioned result to the case of a linear quadratic controller, providing solutions for the optimal control in terms of Riccati backward SDE with random terminal time.

Keywords

• stochastic optimal control
• multiple defaults time
• maximum principle
• linear-quadratic controller