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

Sébastien Choukroun, Andrea Cosso and Huyên Pham

Stochastic Processes and their Applications, 2015, vol. 125, issue 2, 597-633

Abstract: We study a class of reflected backward stochastic differential equations with nonpositive jumps and upper barrier. Existence and uniqueness of a minimal solution are proved by a double penalization 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 affects 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: Backward stochastic differential equations (BSDE) with constrained jumps; Reflected BSDE; Regime-switching jump–diffusion; Hamilton–Jacobi–Bellman Isaacs equation; Controller-and-stopper game (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:125:y:2015:i:2:p:597-633

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DOI: 10.1016/j.spa.2014.09.015

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