Browsing by Author "Ghoul, Abdelhak"

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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.