A general stochastic maximum principle for mixed relaxed-singular control problems
Abstract
Description
We consider in this paper, mixed relaxed-singular stochastic control problems, where the control variable has two components, the first being measure-valued and the second singular. The control domain is not necessarily convex and the system is governed by a nonlinear stochastic differential equation, in which the measure-valued part of the control enters both the drift and the diffusion coefficients. We establish necessary optimality conditions, of the Pontryagin maximum principle type, satisfied by an optimal relaxed-singular control, which exist under general conditions on the coefficients. The proof is based on the strict singular stochastic maximum principle established by Bahlali-Mezerdi, Ekeland's variational principle and some stability properties of the trajectories and adjoint processes with respect to the control variable.
Submitted to Journal of Applied Mathematics and Stochastic Analysis
Submitted to Journal of Applied Mathematics and Stochastic Analysis