THE RELAXED MAXIMUM PRINCIPLE FOR G-STOCHASTIC CONTROL SYSTEMS WITH CONTROLLED JUMPS

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 measure-valued 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 control problem.