Reflected backward stochastic differential equations with resistance

Abstract

In this article, we study a class of reflected backward stochastic differential equations (introduced in El Karoui et al. [Ann. Probab. 25 (1997) 702–737], RBSDE for short) with nonlinear resistance by means of Skorohod’s equation. The advantage of this approach lies in its pathwise nature and, therefore, provides additional information about solutions of RBSDE. As an application of our approach, we will consider reflected backward problems with resistance as well. This class of RBSDEs possess significance in the super-hedging with wealth constraint.