A stochastic Gronwall inequality in random time horizon and its application to BSDE

Abstract

Abstract In this paper, we introduce and prove a stochastic Gronwall inequality in an (unbounded) random time horizon. As an application, we prove a comparison theorem for backward stochastic differential equation (BSDE for short) with random terminal time under a stochastic monotonicity condition.

Keywords

• Gronwall inequality
• Stochastic
• Random time horizon
• Backward stochastic differential equation
• Comparison