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.
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: 28 Mar 2019 *