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.

Reflected BSDEs with nonpositive jumps, and controller-and-stopper games / S. Choukroun, A. Cosso, H. Pham. - In: STOCHASTIC PROCESSES AND THEIR APPLICATIONS. - ISSN 0304-4149. - 125:2(2015 Feb), pp. 597-633. [10.1016/j.spa.2014.09.015]

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

A. Cosso
Penultimo
;
2015

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.
Backward stochastic differential equations (BSDE) with constrained jumps; Controller-and-stopper game; Hamilton-Jacobi-Bellman Isaacs equation; Reflected BSDE; Regimeswitching jump-diffusion; Modeling and Simulation; Statistics and Probability; Applied Mathematics
Settore MAT/06 - Probabilita' e Statistica Matematica
feb-2015
http://www.elsevier.com/locate/issn/03044149
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/931977
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