Nonlinear BSDEs on a general filtration with drivers depending on the martingale part of the solution

Tomasz Klimsiak and Maurycy Rzymowski

Stochastic Processes and their Applications, 2023, vol. 161, issue C, 424-450

Abstract: In the present paper, we consider multidimensional nonlinear backward stochastic differential equations (BSDEs) with a driver depending on the martingale part M of a solution. We assume that the nonlinear term is merely monotone continuous with respect to the state variable. As to the regularity of the driver with respect to the martingale variable, we consider a very general condition which permits path-dependence on “the future” of the process M as well as a dependence of its law (McKean–Vlasov-type equations). For such drivers, we prove the existence and uniqueness of a global solution (i.e. for any maturity T>0) to a BSDE with data satisfying natural integrability conditions.

Keywords: Backward stochastic differential equations; General filtration; Global solutions (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:161:y:2023:i:c:p:424-450

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DOI: 10.1016/j.spa.2023.04.011

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