Backward Stochastic Differential Equations Driven by G-Brownian Motion

2012/06/26 by Hu, Mingshang, Ji, Shaolin, Peng, Shige +1 · 6 citations
#60H10 #60H30 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1206.5889

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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• Infinite horizon quadratic backward stochastic differential equations driven by G-Brownian motion
• Quadratic BSDEs with double constraints driven by G-Brownian motion
• Regularity of Solutions of Mean-Field G-SDEs

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