Shahlar MeherremMokhtar Hafayed2025-10-06201910991514, 014320870143-20871099-151410.1002/oca.2490https://www.scopus.com/inward/record.uri?eid=2-s2.0-85062493112&doi=10.1002%2Foca.2490&partnerID=40&md5=332e376d75dcfd1ec89aa28fefae8b33https://gcris.yasar.edu.tr/handle/123456789/9420In this paper we study stochastic optimal control problem for general McKean-Vlasov–type forward-backward differential equations driven by Teugels martingales associated with some Lévy process having moments of all orders and an independent Brownian motion. The coefficients of the system depend on the state of the solution process as well as of its probability law and the control variable. We establish a set of necessary conditions in the form of Pontryagin maximum principle for the optimal control. We also give additional conditions under which the necessary optimality conditions turn out to be sufficient. The proof of our main result is based on the differentiability with respect to probability law and a corresponding Itô formula. © 2019 Elsevier B.V. All rights reserved.EnglishDerivative With Respect To Probability Law, Maximum Principle, Mckean-vlasov Forward-backward Stochastic Systems With Lévy Process, Optimal Stochastic Control, Teugels Martingales, Brownian Movement, Maximum Principle, Optimal Control Systems, Stochastic Control Systems, Stochastic Systems, Vlasov Equation, Control Variable, Differentiability, Maximum Principle For Optimal Control, Necessary Optimality Condition, Optimal Stochastic Control, Probability Law, Stochastic Optimal Control Problem, Teugels Martingale, Process ControlBrownian movement, Maximum principle, Optimal control systems, Stochastic control systems, Stochastic systems, Vlasov equation, Control variable, Differentiability, Maximum principle for optimal control, Necessary optimality condition, Optimal stochastic control, Probability law, Stochastic optimal control problem, Teugels martingale, Process controlArticle