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

TL;DR

This paper develops a maximum principle for stochastic control problems with multiple random terminal times, providing solutions for linear quadratic controllers and applying the results to interconnected banking systems.

Contribution

It introduces a backward induction method to derive a maximum principle for complex stochastic control problems with multiple random endpoints, including applications to banking networks.

Findings

Derived a maximum principle for multiple random terminal times

Provided explicit solutions for linear quadratic control with Riccati backward SDEs

Applied the theoretical results to interconnected bank systems

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.