Path-Dependent BSDEs with Jumps and Their Connection to PPIDEs

Abstract

We study path-dependent backward stochastic differential equations (BSDEs) with jumps. In this context path-dependence of a BSDE is the dependence of the BSDE-terminal condition and the BSDE-generator of a path of a càdlàg process. We study the path-differentiability of BSDEs of this type and establish a connection to path-dependent PIDEs in terms of the existence of a viscosity solution and the respective Feynman-Kac theorem.

Keywords: path-dependent backward stochastic differential equation; jump diffusion; path-dependent PIDE; functional Feynman-Kac theorem; path-differentiability; viscosity solution; functional Itô formula