Please use this identifier to cite or link to this item: http://archives.univ-biskra.dz/handle/123456789/24884
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dc.contributor.authorLAKHDARI, IMAD EDDINE-
dc.date.accessioned2023-05-02T09:59:32Z-
dc.date.available2023-05-02T09:59:32Z-
dc.date.issued2018-
dc.identifier.urihttp://archives.univ-biskra.dz/handle/123456789/24884-
dc.description.abstractThis thesis presents two research topics, the first one being divided into two parts. In the first part, we study an optimal control problem where the state equation is driven by a normal martingale. We prove a sufficient stochastic maximum and we also show the relationship between stochastic maximum principle and dynamic programming in which the control of the jump size is essential and the corresponding Hamilton-Jacobi-Bellman (HJB) equation in this case is a mixed second order partial differential-difference equation. As an application, we solve explicitly a mean-variance portfolio selection problem. In the second part, we study a non smooth version of the relationship between MP and DPP for systems driven by normal martingales in the situation where the control domain is convex. The second topic, is to characterize sub-game perfect equilibrium strategy of a partially observed optimal control problems for mean-field stochastic differential equations (SDEs) with correlated noises between systems and observations, which is time-inconsistent in the sense that it does not admit the Bellman optimality principle.en_US
dc.language.isoenen_US
dc.subjectNormal martingales, structure equation, stochastic maximum principle, dynamic programming principle, time inconsistency, mean-field control problem, partial information, mean-variance criterion, stochastic systems with jumps.en_US
dc.titleOptimal control for stochastic differential equations governed by normal martingalesen_US
dc.typeThesisen_US
Appears in Collections:Mathématiques

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