Browsing by Author "Miloudi, Hakima"

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    Necessary conditions for partially observed optimal control of general McKean–Vlasov stochastic differential equations with jumps
    (Taylor and Francis Ltd., 2022) Hakima Miloudi; Shahlar Meherrem; Imad Eddine Lakhdari; Mokhtar Hafayed; Miloudi, Hakima; Hafayed, Mokhtar; Meherrem, Shahlar; Lakhdari, Imad Eddine; Eddine Lakhdari, Imad
    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. © 2022 Elsevier B.V. All rights reserved.