LAKHDARI, IMAD EDDINE (2018) Optimal control for stochastic differential equations governed by normal martingales. Doctoral thesis, MOHAMED KHIDER UNIVERSITY, BISKRA.

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Abstract
This 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 HamiltonJacobiBellman (HJB) equation in this case is a mixed second order partial differentialdifference equation. As an application, we solve explicitly a meanvariance 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 subgame perfect equilibrium strategy of a partially observed optimal control problems for meanfield stochastic differential equations (SDEs) with correlated noises between systems and observations, which is timeinconsistent in the sense that it does not admit the Bellman optimality principle.
Item Type:  Thesis (Doctoral) 

Uncontrolled Keywords:  Normal martingales, structure equation, stochastic maximum principle, dynamic programming principle, time inconsistency, meanfield control problem, partial information, meanvariance criterion, stochastic systems with jumps. 
Subjects:  Q Science > QA Mathematics 
Divisions:  Faculté des Sciences Exactes et des Sciences de la Nature et de la Vie > Département de Mathématiques 
Depositing User:  BFSE 
Date Deposited:  27 May 2018 11:08 
Last Modified:  27 May 2018 11:08 
URI:  http://thesis.univbiskra.dz/id/eprint/3677 
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