Reflected BSDEs with jumps in time--dependent convex càdlàg domains
Ouknine, M’hamed Eddahbi, Imade Fakhouri & Youssef . 2020
In the first part of the paper, we study the unique solvability of multidimensional reflected backward
stochastic differential equations (RBSDEs) of Wiener–Poisson type with reflection in the inward spatial
normal direction of a time-dependent adapted càdlàg convex set D = {Dt , t ∈ [0, T ]}. The existence
result is obtained by approximating the solutions of this class of RBSDEs by solutions of BSDEs with
reflection in discretizations of D, while the uniqueness is established by using Itô’s formula. In the second
part of the paper, we show that the solutions of our RBSDEs can be approximated via a non-standard
penalization method.
We focus on solving stochastic differential equations driven by jump processes (SDEJs) with measurable drifts that may exhibit quadratic growth. Our approach leverages
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