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arXiv · 2111.01895

The relaxed maximum principle for G-stochastic control systems with controlled jumps

Hanane Ben Gherbal·Amel Redjil·Omar Kebiri
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Abstract

This paper is concerned with optimal control of systems driven by G-stochastic differential equations (G-SDEs), with controlled jump term. We study the relaxed problem, in which admissible controls are measurevalued processes and the state variable is governed by an G-SDE driven by a counting measure valued process called relaxed Poisson measure such that the compensator is a product measure. Under some conditions on the coefficients, using the G-chattering lemma, we show that the strict and the relaxed control problems have the same value function. Additionally, we derive a maximum principle for this relaxed problem.

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Hanane Ben Gherbal, Amel Redjil, Omar Kebiri. 2021-11-02. The relaxed maximum principle for G-stochastic control systems with controlled jumps. https://arxiv.org/abs/2111.01895

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