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

TL;DR

This paper develops a relaxed maximum principle for G-stochastic control systems with jumps, showing equivalence of strict and relaxed control problems and providing optimality conditions.

Contribution

It introduces a relaxed control framework for G-SDEs with jumps and establishes a maximum principle, extending stochastic control theory under model uncertainty.

Findings

Strict and relaxed control problems share the same value function.

Derived a maximum principle for the relaxed control problem.

Established conditions under which the relaxed and strict controls are equivalent.

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.