Necessary conditions for partially observed optimal control of general McKean–Vlasov stochastic differential equations with jumps

In this paper, we establish necessary conditions of optimality for partially observed optimal control problems of Mckean–Vlasov type. The system is described by a controlled stochastic differential equation governed by Poisson random measure and an independent Brownian motion. The coefficients of the McKean–Vlasov system depend on the state of the solution process as well as of its probability law and the control variable. The proof of our result is based on Girsanov's theorem, variational equations and derivatives with respect to probability measure under convexity assumption. At the end of this paper, we apply our stochastic maximum principle to study partially observed linear quadratic control problem of McKean–Vlasov type with jumps and derive the explicit expression of the optimal control

A general characterization of the stochastic optimal combined control of mean field stochastic systems with application

In this paper, a general characterization of the optimal stochastic combined control for mean-field jump-systems is derived by applying mixed convex-spike perturbation method. The diffusion coefficient depends on the continuous control variable and the coDepartment of Mathematics, Yasar University, University aven, Agaclı Yol No. 35-57, Izmir, Turkey; Laboratory of Applied Mathematics, Biskra University, PO. Box 145, Biskra, 07000, Algeri

On optimal control of mean-field stochastic systems driven by Teugels martingales via derivative with respect to measures

This paper deals with partial information stochastic optimal control problem for general controlled mean-field systems driven by Teugels martingales associated with some Levy process having moments of all orders, and an independent Brownian motion. The coTurkiye Bilimsel ve Teknolojik Arastirma Kurumu project [2221]Automation & Control SystemsAutomation & Control System

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

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 throuAutomation & Control SystemsAutomation & Control System

On optimal singular control problem for general Mckean-Vlasov differential equations: Necessary and sufficient optimality conditions

In this paper, we derive the necessary and sufficient conditions for optimal singular control for systems governed by general controlled McKean-Vlasov differential equations, in which the coefficients depend on the state of the solution process as well asTUBITAKTurkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [2221]Automation & Control Systems; Operations Research & Management Science; Mathematics, AppliedAutomation & Control Systems; Operations Research & Management Science; Mathematic

A McKean-Vlasov optimal mixed regular-singular control problem for nonlinear stochastic systems with Poisson jump processes

In this paper, we develop the necessary conditions of optimality for a new class of mixed regular-singular control problem for nonlinear forward-backward stochastic systems with Poisson jump processes of McKean-Vlasov type. The coefficients of the systemLaboratory of Applied Mathematics, Biskra University, PO Box 145, Biskra, 07000, Algeria; Graduate School of Science and Technology, Tokai University 9-1-1, Toroku, Kumamoto, 862-8652, Japan; Yasar University, University aven, Agacli Yol No. 35-57, Izmir

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

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. UnderLaboratory of Applied Mathematics, Biskra University, P.O. Box 145, Biskra, 07000, Algeria; Department of Mathematics, Faculty of Sciences and Letters, Yasar University, İzmir, Turke

On optimal solutions of general continuous-singular stochastic control problem of McKean-Vlasov type

In this paper, we establish general necessary optimality conditions for stochastic continuous-singular control of McKean-Vlasov type equations. The coefficients of the state equation depend on the state of the solution process as well as of its probabilitLaboratory of Mathematical Analysis, Probabilities and Optimizations, University of Biskra, Po. Box 145, Biskra, Algeria; Department of Mathematics, Yasar University, University aven, Agaclı Yol No. 35-57, Izmir, Turkey; School of Basic Sciences, Indian