Title: Variational principle for stochastic singular control of mean-field Lévy-forward-backward system driven by orthogonal Teugels martingales with application

Authors: Mokhtar Hafayed; Shahlar Meherrem; Deniz H. Gucoglu; Saban Eren

Addresses: Laboratory of Applied Mathematics, Biskra University, P.O. Box 145, Biskra 07000, Algeria ' Department of Mathematics, Faculty of Sciences and Letters, Yasar University, ?zmir, Turkey ' Department of Mathematics, Faculty of Sciences and Letters, Yasar University, ?zmir, Turkey ' Department of Mathematics, Faculty of Sciences and Letters, Yasar University, ?zmir, Turkey

Abstract: We consider stochastic singular control for mean-field forward-backward stochastic differential equations, driven by orthogonal Teugels martingales associated with some Lévy processes having moments of all orders and an independent Brownian motion. Under partial information, necessary and sufficient conditions for optimality in the form of maximum principle for this mean-field system are established by means of convex variation methods and duality techniques. As an illustration, this paper studies a partial information mean-variance portfolio selection problem driven by orthogonal Teugels martingales associated with gamma process as Lévy process of bounded variation.

Keywords: controlled forward-backward system; maximum principle; orthogonal Teugels martingales; Lévy processes; singular control; mean-field stochastic system; partial information; gamma process.

DOI: 10.1504/IJMIC.2017.085944

International Journal of Modelling, Identification and Control, 2017 Vol.28 No.2, pp.97 - 113

Received: 27 Aug 2016
Accepted: 23 Oct 2016
Published online: 18 Aug 2017 *

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