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arXiv · 0801.4669

A general stochastic maximum principle for mixed relaxed-singular control problems

Seid Bahlali
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Abstract

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.

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Seid Bahlali. 2008-08-28. A general stochastic maximum principle for mixed relaxed-singular control problems. https://arxiv.org/abs/0801.4669

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