Reflected BSDEs with nonpositive jumps, and controller-and-stopper gamesReport as inadecuate

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1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires 2 Dipartimento di Matematica, Politecnico di Milano Dipartimento di Matematica -F. Brioschi- 3 CREST - Centre de Recherche en Économie et Statistique

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.

Keywords : controller-and-stopper game Backward stochastic differential equations BSDE with constrained jumps reflected BSDE regime-switching jump-diffusion Hamilton-Jacobi-Bellman Isaacs equation controller-and-stopper game.

Author: Sébastien Choukroun - Andrea Cosso - Huyen Pham -



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