L^p Solutions of One-Dimensional Backward Stochastic Differential Equations with Continuous Coefficients

Abstract

In this article, we study one-dimensional backward stochastic differential equations with continuous coefficients. We show that if the generator f is uniformly continuous in (y, z), uniformly with respect to (t, ω), and if the terminal value ξ ∈L ^p (Ω, ℱ _T , P) with 1 < p ≤ 2, the backward stochastic differential equation has a unique L ^p solution.

Keywords:

• Backward stochastic differential equations
• L ^p solution
• Uniformly continuous

Mathematics Subject Classification:

• 60H10
• 60H30

Research supported by NSFC under grant 10325101, Basic Research Program of China (973 Program) with Grant No. 2007CB814904, Natural Science Foundation of Zhejiang Province under grant Y605478 and Y606667.

The author would like to thank an anonymous referee for the precise comments and helpful suggestions offered, as well as Professor Shanjian Tang and Dr. Kai Du for their valuable comments and helpful discussions.