Backward Stochastic Differential Equations for a Single Jump Process

Abstract

We consider backward stochastic differential equations (BSDEs) related to a finite continuous time single jump process. We prove the existence and uniqueness of solutions when the coefficients satisfy Lipschitz continuity conditions. A comparison theorem for these solutions is also given. Applications to the theory of nonlinear expectations are then investigated.

Keywords:

• Backward stochastic differential equation
• Comparison theorem
• Dynamic risk measure
• Nonlinear expectation
• Single jump process

Mathematics Subject Classification:

• 60H10
• 60G42
• 65C30

Acknowledgments

Robert Elliott wishes to thank the Australian Research Council for support.