Backward Stochastic Differential Equations Driven by G-Brownian Motion

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.

27 pages

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• Comparison Theorem, Feynman-Kac Formula and Girsanov Transformation for BSDEs Driven by G-Brownian Motion
• Supermartingale Decomposition Theorem under G-expectation
• $G$-martingale representation in the $G$-L'evy setting
• G-Expectation Weighted Sobolev Spaces, Backward SDE and Path Dependent PDE
• Some Norm Estimates for Semimartingales
• A stochastic recursive optimal control problem under the G-expectation framework
• A note on pricing of contingent claims under G-expectation
• Representation theorem for generators of BSDEs driven by G-Brownian motion and its applications
• Stochastic Optimization Theory of Backward Stochastic Differential Equations Driven by G-Brownian Motion
• A Stochastic Maximum Principle for Processes Driven by G-Brownian Motion and Applications to Finance
• On monotonicity and order-preservation for multidimensional G-diffusion processes
• The G-convex Functions Based on the Nonlinear Expectations Defined by G-BSDEs