𝕃p solutions of reflected backward stochastic differential equations with jumps

Abstract

Given p ∈ (1, 2), we study 𝕃p-solutions of a reflected backward stochastic differential equation with jumps (RBSDEJ) whose generator g is Lipschitz continuous in (y, z, u). Based on a general comparison theorem as well as the optimal stopping theory for uniformly integrable processes under jump filtration, we show that such a RBSDEJ with p-integrable parameters admits a unique 𝕃p solution via a fixed-point argument. The Y -component of the unique 𝕃p solution can be viewed as the Snell envelope of the reflecting obstacle 𝔏 under g-evaluations, and the first time Y meets 𝔏 is an optimal stopping time for maximizing the g-evaluation of reward 𝔏.