Optimality Conditions for Relaxed Control Problems Governed by Forward-Backward Doubly Stochastic Differential Equations with Jumps

AbdulRahman Al-Hussein* and Boulakhras Gherbal

This talk is concerned with the maximum principle for a relaxed control problem with jumps, which is governed by a fully coupled multi-dimensional forward-backward doubly stochastic differential equation with Poisson jumps.\newline We establish in particular necessary and sufficient optimality conditions for this control problem with respect to the relaxed controls, which are measure-valued processes.

Mathematics Subject Classification: 60H10 93E20 60G55

Keywords: Poisson process; maximum principle; relaxed control; forward-backward doubly stochastic differential equation; adjoint equations.

Minisymposion: Analysis and Control of Evolution Equations and Inclusions