Backward Stochastic Differential Equations Driven by G-Brownian Motion

TL;DR

This paper investigates backward stochastic differential equations driven by G-Brownian motion, establishing existence and uniqueness of solutions using G-framework stochastic calculus, which differs from classical methods.

Contribution

It introduces a new class of BSDEs driven by G-Brownian motion and proves their well-posedness under Lipschitz conditions, expanding stochastic calculus in G-framework.

Findings

Existence and uniqueness of solutions (Y,Z,K) for G-BSDEs.

Development of methods using G-framework stochastic calculus.

Extension of classical BSDE theory to G-Brownian motion context.

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.