A global maximum principle for optimal control of general mean-field forward-backward stochastic systems with jumps

Hao, Tao; Meng, Qingxin

ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 87.

Suite au passage du modèle économique de la revue en S20, le texte intégral des articles des années 2019 et 2020 est accessible uniquement sur le site de l'éditeur et est réservé aux abonnés.

In this paper we prove a maximum principle of optimal control problem for a class of general mean-field forward-backward stochastic systems with jumps in the case where the diffusion coefficients depend on control, the control set does not need to be convex, the coefficients of jump terms are independent of control as well as the coefficients of mean-field backward stochastic differential equations depend on the joint law of (X(t), Y (t)). Since the coefficients depend on measure, higher mean-field terms could be involved. In order to analyse them, two new adjoint equations are brought in and several new generic estimates of their solutions are investigated. Utilizing these subtle estimates, the second-order expansion of the cost functional, which is the key point to analyse the necessary condition, is obtained, and where after the stochastic maximum principle. An illustrative application to mean-field game is considered.

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