Lp Solutions of -Backward Stochastic Differential Equations with Continuous Coefficients

Year 2015, Volume: 36 Issue: 3, 2234 - 2241, 13.05.2015

Mojtaba Malekı , Elham Dastranj Reza Hejazı

Abstract

Abstract. In this paper, we study -backward stochastic differential equations with continuous coefficients. We give existence and uniqueness results for G-backward stochastic differential equations, when the generator  is uniformly continuous in , and the terminal value with .

We consider the G-backward stochastic differential equations driven by a G-Brownian motion in the following form:

                                                           (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

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