Generalized reflected backward stochastic differential equations

Abstract

In this paper, existence of a generalized reflected backward stochastic differential equation in a general convex domain is studied. A general discrete approximation scheme for this equation is constructed and then some examples of approximation schemes are presented. Moreover, applications to obstacle problem with Neumann condition for partial differential equations are given.

Keywords:

• reflected BSDE
• discrete approximation methods
• viscosity solution

AMS Subject Classification:

• 60H10
• 60Gxx
• 35K20