Liste de Publications et résumés

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Mes intérêts de recherche sont sur la théorie de contrôle stochastiques et la théorie des équations différentielles stochastiques rétrogrades.

Plus précisément : 

• Les  équations différentielles stochastiques Progressives rétrogrades (EDSPR).

• La théorie de contrôle stochastiques avec des systèmes de EDSPR couplées.                                                          

• Les  équations différentielles doublement stochastiques rétrogrades  (EDDSR) : existence et unicité des solutions.

• Les équations au dérivées partielles stochastiques  (EDPS).

1. K.Bahlali, B.Mansouri ,R.Gatt, A.Mtiraoui.    Backward doubly SDEs and SPDEs with superlinear growth generators.   Stochastics and Dynamics           Vol. 17, No. 1 (2016)

2. K.Bahlali, O.Kebiri, A.Mtiraoui.     Existence of an optimal control for a system driven by a degenerate coupled forward-backward stochastic diff.erential equations C. R. Acad. Sci. Paris, Ser. I  (2017)

3. K.Bahlali, O.Kebiri, B. Mezerdi, A.Mtiraoui.       Existence of an Optimal Control for a coupled FBSDE with a non degenerate diffusion coefficient.    Stochastics, DOI : 10.1080/17442508.2018.1427750 (2018)

4. EDSRs appliquées à la finance et aux EDPs. Mémoire de master préparé sous la direction de M. Saïd Hamadène.  Le fichier pdf est en bas de la page  (mémoire de master.pdf).

5.  I. Etude des EDDSRs surlinéaires.  II. Contrôle des EDSPRs couplées. Manuscrit de thèse sous la direction de

 M. Khaled Bahlali.   Le fichier pdf est en bas de la page  (these-à-publier.pdf).

         Backward doubly SDEs and SPDEs with superlinear growth generators.

K.Bahlali B.Mansouri R.Gatt A.Mtiraoui

Abstract

We deal with multidimensional backward doubly stochastic differential equations (BDSDEs) with a superlinear growth generator and a square integrable terminal datum. We introduce new local conditions on the generator and then show that they ensure the existence and uniqueness as well as the stability of solutions. Our work goes beyond the previous results on the subject. Although we are focused on multidimensional case, the uniqueness result we establish is new in one-dimensional too. As an application, we establish the existence and uniqueness of probabilistic solutions to some semilinear stochastic partial differential equations (SPDEs) with superlinear growth gernerator. By probabilistic solution, we mean a solution which is representable throughout a BDSDEs.

Existence of an Optimal Control for a  coupled Forward-Backward Stochastic Differential Equations-Degenerate Case

K.Bahlali O.Kebiri A.Mtiraoui

Abstract

We establish the existence of an optimal control for systems driven by a coupled forward-backward stochastic differential equations (FBDSEs in short) under the so-called G-monotonic condition on the generator.  The (nonlinear) cost functional is defined by the backward component at the initial time. We first establish the existence of a relaxed  optimal feedback control. The existence of a strict control is obtained by assuming the Filippov convexity condition.

Existence of an Optimal Control for a coupled FBSDE with a non degenerate diffusion coefficient

K.Bahlali O.Kebiri B.Mezerdi A.Mtiraoui

Abstract

We consider a controlled system driven by a coupled forward-backward stochastic differential equation (FBSDE) with a non degenerate diffusion matrix. The cost functional is defined by the solution of the controlled backward stochastic differential equation (BSDE), at the initial time. Our goal is to find an optimal control which minimizes the cost functional. The method consists to construct a sequence of approximating controlled systems for which we show the existence of a sequence of feedback optimal controls. By passing to the limit, we establish the existence of a relaxed optimal control to the initial problem. The existence of a strict control follows from the Filippov convexity condition.