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Backward SDEs with constrained jumps and Quasi-Variational Inequalities

Abstract : We consider a class of backward stochastic differential equations (BSDEs) driven by Brownian motion and Poisson random measure, and subject to constraints on the jump component. We prove the existence and uniqueness of the minimal solution for the BSDEs by using a penalization approach. Moreover, we show that under mild conditions the minimal solutions to these constrained BSDEs can be characterized as the unique viscosity solution of quasi-variational inequalities (QVIs), which leads to a probabilistic representation for solutions to QVIs. Such a representation in particular gives a new stochastic formula for value functions of a class of impulse control problems. As a direct consequence we obtain a numerical scheme for the solution of such QVIs via the simulation of the penalized BSDEs.
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https://hal.archives-ouvertes.fr/hal-00283407
Contributor : Huyên Pham <>
Submitted on : Thursday, May 29, 2008 - 9:47:16 PM
Last modification on : Wednesday, December 9, 2020 - 3:07:44 PM
Long-term archiving on: : Friday, May 28, 2010 - 8:42:35 PM

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  • HAL Id : hal-00283407, version 1
  • ARXIV : 0805.4676

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Idris Kharroubi, Jin Ma, Huyen Pham, Jianfeng Zhang. Backward SDEs with constrained jumps and Quasi-Variational Inequalities. 2008. ⟨hal-00283407⟩

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