Lp Solution of Reflected BSDEs with One Continuous Barrier and Quasi-linear Growth Generators

Abstract

This paper is devoted to solving a reflected backward stochastic differential equation (BSDE in short) with one continuous barrier and a quasi-linear growth generator g, which has a linear growth in (y, z), except the upper direction in case of y < 0, and is more general than the usual linear growth generator. By showing the convergence of a penalization scheme we prove existence and comparison theorem of the minimal L^p (p > 1) solutions for the reflected BSDEs. We also prove that the minimal L^p solution can be approximated by a sequence of L^p solutions of certain reflected BSDEs with Lipschitz generators.