Browsing by Author "Hafayed, Mokhtar"

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A general characterization of the stochastic optimal combined control of mean field stochastic systems with application
(Springer Berlin Heidelberg, 2018) Shahlar Meherrem; Mokhtar Hafayed; Deniz Hasan Guçoglu; Şaban Eren; Hafayed, Mokhtar; Meherrem, Shahlar; Gucoglu, Deniz H.; Eren, Saban
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 control domain is not necessary convex. In our combined mean-field control problem we discuss two classes of jumps for the state processes the inaccessible jumps which caused by Poisson martingale measure and the predictable ones which caused by the singularity of the control variable. Markowitz’s mean–variance portfolio selection problem with intervention control is discussed. © 2020 Elsevier B.V. All rights reserved.
Citation - WoS: 14
Citation - Scopus: 15
A McKean-Vlasov optimal mixed regular-singular control problem for nonlinear stochastic systems with Poisson jump processes
(Elsevier B.V., 2016) Mokhtar Hafayed; Samira Boukaf; Yan Shi; Shahlar Meherrem; Boukaf, Samira; Hafayed, Mokhtar; Shi, Yan; Meherrem, Shahlar
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 system and the performance functional depend not only on the state process but also its marginal law of the state process through its expected value. The control variable has two components the first being absolutely continuous and the second singular control. Our optimality conditions for these McKean-Vlasov[U+05F3]s systems are established by means of convex perturbation techniques for both continuous and singular parts. In our class of McKean-Vlasov control problem there are two types of jumps for the state processes the inaccessible ones which come from the Poisson martingale part and the predictable ones which come from the singular control part. © 2017 Elsevier B.V. All rights reserved.
Citation - WoS: 1
Citation - Scopus: 1
A STOCHASTIC MAXIMUM PRINCIPLE FOR GENERAL MEAN-FIELD SYSTEM WITH CONSTRAINTS
(AMER INST MATHEMATICAL SCIENCES-AIMS, 2025) Shahlar Meherrem; Mokhtar Hafayed; Hafayed, Mokhtar; Meherrem, Shahlar
In this paper we study the optimal control of a general mean-field stochastic differential equation with constraints. We establish a set of necessary conditions for the optimal control where the coefficients of the controlled system depend nonlinearly on both the state process as well as of its probability law. The control domain is not necessarily convex. The proof of our main result is based on the first-order and second-order derivatives with respect to measure in the Wasserstein space of probability measures and the variational principle. We prove Peng's type necessary optimality conditions for a general mean-field system under state constraints. Our result generalizes the stochastic maximum principle of Buckdahn et al. [2] to the case with constraints.
Citation - WoS: 11
Citation - Scopus: 10
Maximum principle for optimal control of McKean-Vlasov FBSDEs with Levy process via the differentiability with respect to probability law
(WILEY, 2019) Shahlar Meherrem; Mokhtar Hafayed; Hafayed, Mokhtar; Meherrem, Shahlar
In this paper we study stochastic optimal control problem for general McKean-Vlasov-type forward-backward differential equations driven by Teugels martingales associated with some Levy 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 Ito formula.
Citation - WoS: 9
Citation - Scopus: 9
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.
Citation - WoS: 5
Citation - Scopus: 5
On optimal control of mean-field stochastic systems driven by Teugels martingales via derivative with respect to measures
(TAYLOR & FRANCIS LTD, 2020) Mokhtar Hafayed; Shahlar Meherrem; Hafayed, Mokhtar; Meherrem, Shahlar
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 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 result is based on the derivative with respect to the probability law by applying Lions derivatives and a corresponding Ito formula. As an application conditional mean-variance portfolio selection problem in incomplete market where the system is governed by some Gamma process is studied to illustrate our theoretical results.
Citation - WoS: 19
Citation - Scopus: 19
On optimal singular control problem for general Mckean-Vlasov differential equations: Necessary and sufficient optimality conditions
(John Wiley and Sons Ltd vgorayska@wiley.com Southern Gate Chichester West Sussex PO19 8SQ, 2018) Mokhtar Hafayed; Shahlar Meherrem; Şaban Eren; Deniz Hasan Guçoglu; Hafayed, Mokhtar; Meherrem, Shahlar; Eren, Saban; Gucoglu, Deniz Hasan
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 as of its law and control. The control domain is assumed to be convex. The control variable has 2 components ie the first being absolutely continuous and the second being singular. The proof of our result is based on the derivative of the solution process with respect to the probability law and a corresponding Itô formula. Finally an example is given to illustrate the theoretical results. © 2018 Elsevier B.V. All rights reserved.
Citation - WoS: 6
Citation - Scopus: 6
On optimal solutions of general continuous-singular stochastic control problem of McKean-Vlasov type
(WILEY, 2020) Lina Guenane; Mokhtar Hafayed; Shahlar Meherrem; Syed Abbas; Guenane, Lina; Hafayed, Mokhtar; Meherrem, Shahlar; Abbas, Syed
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 probability law and the control variable. The coefficients of the system are nonlinear and depend explicitly on the absolutely continuous component of the control. The control domain under consideration is not assumed to be convex. The proof of our main result is based on the first- and second-order derivatives with respect to measure in Wasserstein space of probability measures and by using variational method.
Citation - WoS: 6
Citation - Scopus: 6
On partially observed optimal singular control of McKean–Vlasov stochastic systems: Maximum principle approach
(John Wiley and Sons Ltd, 2022) Nour El Houda Abada; Mokhtar Hafayed; Shahlar Meherrem; Hafayed, Mokhtar; Meherrem, Shahlar; Abada, Nour El Houda
In this paper we study partially observed optimal stochastic singular control problems of general Mckean–Vlasov type with correlated noises between the system and the observation. The control variable has two components the first being absolutely continuous and the second is a bounded variation nondecreasing continuous on the right with left limits. The dynamic system is governed by Itô-type controlled stochastic differential equation. The coefficients of the dynamic depend on the state process and of its probability law and the continuous control variable. In terms of a classical convex variational techniques we establish a set of necessary conditions of optimal singular control in the form of maximum principle. Our main result is proved by applying Girsanov's theorem and the derivatives with respect to probability law in Lions' sense. To illustrate our theoretical result we study partially observed linear-quadratic singular control problem of McKean–Vlasov type. © 2022 Elsevier B.V. All rights reserved.
Citation - WoS: 2
Citation - Scopus: 2
On Peng's type maximum principle for optimal control of mean-field stochastic differential equations with jump processes
(INDERSCIENCE ENTERPRISES LTD, 2019) Shahlar Meherrem; Mokhtar Hafayed; Syed Abbas; Hafayed, Mokhtar; Meherrem, Shahlar; Abbas, Syed
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 through their expected values. We assume that the control set is a general open set that is not necessary convex. The control variable is allowed to enter into both diffusion and jump terms. We extend the maximum principle of Buckdahn et al. (2011) to jump case.
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.
Citation - WoS: 3
Citation - Scopus: 3
Variational principle for stochastic singular control of mean-field Levy-forward-backward system driven by orthogonal Teugels martingales with application
(INDERSCIENCE ENTERPRISES LTD, 2017) Mokhtar Hafayed; Shahlar Meherrem; Deniz H. Gucoglu; Saban Eren; Hafayed, Mokhtar; Meherrem, Shahlar; Gucoglu, Deniz H.; Eren, Saban
We consider stochastic singular control for mean-field forward-backward stochastic differential equations driven by orthogonal Teugels martingales associated with some Levy processes having moments of all orders and an independent Brownian motion. Under partial information necessary and sufficient conditions for optimality in the form of maximum principle for this mean-field system are established by means of convex variation methods and duality techniques. As an illustration this paper studies a partial information mean-variance portfolio selection problem driven by orthogonal Teugels martingales associated with gamma process as Levy process of bounded variation.