EDS Rétrogrades et Contrôle Stochastique Séquentiel en Temps Continu en Finance

Abstract : We study the link between Backward SDEs and some stochastic optimal control problems and their application to mathematical finance. In the first part we focus on the BSDE representation of solution to impulse control and optimal switching. We first introduce the notion of constrained BSDEs with jumps and prove that it gives a representation of solutions to Markovian impulse control problems. We then bind these contrained BSDEs to BSDEs with oblique reflexion and optimal switching problems. In the secoond part, we study the time discretization of the previous BSDEs. We first state a discretization of constrained BSDE using the approximation given by the penalized BSDEs. We the provide a speed convergence for the natural scheme associated to BSDEs with oblique reflections. Finally, in the third part, we consider a liquidation problem under execution risk and cost. We characterize the associated value function as the minimal solution to the associated quasi-variational inequality.
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https://pastel.archives-ouvertes.fr/tel-00439542
Contributor : Idris Kharroubi <>
Submitted on : Monday, December 7, 2009 - 5:34:42 PM
Last modification on : Tuesday, May 14, 2019 - 11:02:17 AM
Long-term archiving on : Thursday, October 18, 2012 - 10:10:44 AM

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  • HAL Id : tel-00439542, version 1

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Idris Kharroubi. EDS Rétrogrades et Contrôle Stochastique Séquentiel en Temps Continu en Finance. Mathématiques [math]. Université Paris-Diderot - Paris VII, 2009. Français. ⟨tel-00439542⟩

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