Abstract
Given p â (1, 2), we study đp-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 đp solution via a fixed-point argument. The Y -component of the unique đp solution can be viewed as the Snell envelope of the reflecting obstacle đ under g-evaluations, and the first time Y meets đ is an optimal stopping time for maximizing the g-evaluation of reward đ.
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