Backward Stochastic Differential Equations Driven by G-Brownian Motion

Mingshang Hu; Shaolin Ji; Shige Peng; Yongsheng Song

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arXiv · 1206.5889

Backward Stochastic Differential Equations Driven by G-Brownian Motion

Mingshang Hu·Shaolin Ji·Shige Peng·Yongsheng Song

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Abstract

In this paper, we study backward stochastic differential equations driven by a G-Brownian motion. The solution of such new type of BSDE is a triple (Y,Z,K) where K is a decreasing G-martingale. Under a Lipschitz condition for generator f and g in Y and Z. The existence and uniqueness of the solution (Y,Z,K) is proved. Although the methods used in the proof and the related estimates are quite different from the classical proof for BSDEs, stochastic calculus in G-framework plays a central role.

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Mingshang Hu, Shaolin Ji, Shige Peng, Yongsheng Song. 2012-06-26. Backward Stochastic Differential Equations Driven by G-Brownian Motion. https://arxiv.org/abs/1206.5889

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