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

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 measur...

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Bibliographic Details
Published in:arXiv.org 2021-11
Main Authors: Hanane Ben Gherbal, Redjil, Amel, Kebiri, Omar
Format: Article
Language:English
Subjects:
Compensators
Control systems
Differential equations
Maximum principle
Optimal control
Stochastic processes
Online Access:Get full text
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Summary: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.
ISSN:2331-8422