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, and ad hoc maximum principle for an optimal control problem with multiple random terminal times. Therefore we 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. Eventually all the above results are applied to a system of interconnected banks.