Title: On Peng's type maximum principle for optimal control of mean-field stochastic differential equations with jump processes

Authors: Shahlar Meherrem; Mokhtar Hafayed; Syed Abbas

Addresses: Department of Mathematics, Yasar University, University Aven, Agaclı Yol No. 35–57, Izmir, Turkey ' Laboratory of Applied Mathematics, Biskra University, P.O. Box 145, Biskra 07000, Algeria ' School of Basic Sciences, Indian Institute of Technology Mandi, Mandi H.P. 175001, India

Abstract: In this paper, we investigate the Peng's type optimal control problems for stochastic differential equations of mean-field type with jump processes. The coefficients of the system contain not only the state process but also its marginal distribution through their expected values. We assume that the control set is a general open set that is not necessary convex. The control variable is allowed to enter into both diffusion and jump terms. We extend the maximum principle of Buckdahn et al. (2011) to jump case.

Keywords: mean-field jump systems; stochastic optimal control; Peng's maximum principle; spike variation method; second-order adjoint equation; Poisson martingale measure.

DOI: 10.1504/IJMIC.2019.098782

International Journal of Modelling, Identification and Control, 2019 Vol.31 No.3, pp.245 - 258

Received: 26 Jan 2018
Accepted: 08 Apr 2018
Published online: 02 Apr 2019 *

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