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

Francesco Cordoni; Luca Di Persio; Francesco Cordoni; Luca Di Persio

doi:10.3934/mine.2020025

Mathematics in Engineering

2020, Volume 2, Issue 3: 557-583. doi: 10.3934/mine.2020025

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Research article

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

Francesco Cordoni ,
Luca Di Persio ^,

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

Received: 01 April 2020 Accepted: 02 May 2020 Published: 08 May 2020

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.
- stochastic optimal control,
- multiple defaults time,
- maximum principle,
- linear-quadratic controller
Citation: Francesco Cordoni, Luca Di Persio. A maximum principle for a stochastic control problem with multiple random terminal times[J]. Mathematics in Engineering, 2020, 2(3): 557-583. doi: 10.3934/mine.2020025

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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.

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