Solutions of G-Backward Stochastic Differential Equations with Continuous Coefficients

In this paper, we study G-backward stochastic differential equations with continuous coefficients. Mingshang Hu, Shaolin Ji, Shige Peng, Yongsheng Song [1] proved an existence and uniqueness result when and are Lipschitz conditions in and in the G-framework. We give existence and uniqueness results for G-backward stochastic differential equations, when the generator is uniformly continuous in y, z, and the terminal value ξ ∈ L with 1 2. We consider the G-backward stochastic differential equations driven by a GBrownian motion in the following form: !, , #! $ !, , # B s 〈 〉 % # $ % &$ % & ,(1)where , and & are unknown and the random function , called the generator,and the random variable , called terminal value, are given. Our main result of this paper is the existence and uniqueness of a solution , ,& for (1) in the G framework.

Keywords:

G-expectation , G-Brownian motion , G-martingale , G-Backward stochastic differential equations , '( solution