Browsing by Author "Lakhdari, Imad Eddine"

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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.
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    Pointwise Second-Order Necessary Conditions for Stochastic Optimal Control with Jump Diffusions
    (Springer Science and Business Media Deutschland GmbH, 2023) Abdelhak Ghoul; Mokhtar Hafayed; Imad Eddine Lakhdari; Shahlar Meherrem; Ghoul, Abdelhak; Hafayed, Mokhtar; Lakhdari, Imad Eddine; Meherrem, Shahlar
    In this paper we establish a second-order necessary conditions for stochastic optimal control for jump diffusions. The controlled system is described by a stochastic differential systems driven by Poisson random measure and an independent Brownian motion. The control domain is assumed to be convex. Pointwise second-order maximum principle for controlled jump diffusion in terms of the martingale with respect to the time variable is proved. The proof of the main result is based on variational approach using the stochastic calculus of jump diffusions and some estimates on the state processes. © 2023 Elsevier B.V. All rights reserved.