Title: Optimal continuous-singular control of stochastic McKean-Vlasov system in Wasserstein space of probability measures

Authors: Samira Boukaf; Lina Guenane; Mokhtar Hafayed

Addresses: Laboratory of Mathematical Analysis, Probability and Optimizations, University of Biskra, Biskra, P.O. Box 145, Biskra 07000, Algeria ' Laboratory of Mathematical Analysis, Probability and Optimizations, University of Biskra, Biskra, P.O. Box 145, Biskra 07000, Algeria ' Laboratory of Mathematical Analysis, Probability and Optimizations, University of Biskra, Biskra, P.O. Box 145, Biskra 07000, Algeria

Abstract: In this paper, we study the local form of maximum principle for optimal stochastic continuous-singular control of nonlinear Itô stochastic differential equation of McKean-Vlasov type, with incomplete information. The coefficients of the system are nonlinear and depend on the state process as well as its probability law. The control variable is allowed to enter into both drift and diffusion coefficients. The action space is assumed to be convex. The proof of our local maximum principle is based on the differentiability with respect to the probability law in Wasserstein space of probability measures with some appropriate estimates.

Keywords: derivative with respect to probability law; optimal continuous-singular control; McKean-Vlasov stochastic system; Wasserstein space of probability measures; maximum principle.

DOI: 10.1504/IJDSDE.2022.126543

International Journal of Dynamical Systems and Differential Equations, 2022 Vol.12 No.4, pp.301 - 315

Received: 23 Jul 2021
Accepted: 03 Sep 2021
Published online: 28 Oct 2022 *

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