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In the present paper we derive, via a backward induction technique, and adhoc maximum principle for an optimal control problem with multiple randomterminal times. Therefore we apply the aforementioned result to the case of alinear quadratic controller, providing solutions for the optimal control interms of Riccati backward SDE with random terminal time. Eventually all theabove results are applied to a system of interconnected banks.

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