Reflected BSDEs with nonpositive jumps, and controller-and-stopper games

Abstract : We study a class of reflected backward stochastic differential equations with nonpositive jumps and upper barrier. Existence and uniqueness of a minimal solution is proved by a double pena\-lization approach under regularity assumptions on the obstacle. In a suitable regime switching diffusion framework, we show the connection between our class of BSDEs and fully nonlinear variational inequalities. Our BSDE representation provides in particular a Feynman-Kac type formula for PDEs associated to general zero-sum stochastic differential controller-and-stopper games, where control affect both drift and diffusion term, and the diffusion coefficient can be degenerate. Moreover, we state a dual game formula of this BSDE minimal solution involving equivalent change of probability measures, and discount processes. This gives in particular a new representation for zero-sum stochastic differential controller-and-stopper games.
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Pré-publication, Document de travail
2013
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https://hal.archives-ouvertes.fr/hal-00853988
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Dernière modification le : mardi 30 mai 2017 - 01:17:30
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  • HAL Id : hal-00853988, version 1
  • ARXIV : 1308.5511

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Sébastien Choukroun, Andrea Cosso, Huyen Pham. Reflected BSDEs with nonpositive jumps, and controller-and-stopper games. 2013. 〈hal-00853988〉

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