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

Department of Computer Science, University of Verona, Strada le Grazie, 15, Verona, 37134, Italy

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.
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