Generalized reflected BSDEs driven by a Levy process and an obstacle problem for PDIEs with a nonlinear Neumann boundary condition

作者：Ren Yong^*; El Otmani Mohamed

来源：Journal of Computational and Applied Mathematics, 2010, 233(8): 2027-2043.

DOI：10.1016/j.cam.2009.09.037

• Reflected BSDEs
• Generalized BSDEs
• Teugels martingale
• Levy process
• Viscosity solution

In this paper, we derive the existence and Uniqueness Of the Solution for a class of generalized reflected backward stochastic differential equations (GRBSDEs in short) driven by a Levy process,which involve the integral with respect to a continuous process by means of the Snell envelope, the penalization method and the fixed point theorem. In addition, we obtain the comparison theorem for the solutions of the GRBSDEs. As an application, we give a probabilistic formula for the viscosity solution of an obstacle problem for a class of partial differential-integral equations (PDIEs in short) with a nonlinear Neumann boundary condition.

• 出版日期2010-2-15