Discrete-time approximation for backward stochastic differential equations driven by $G$-Brownian motion

Abstract

In this paper, we study the discrete-time approximation schemes for a class of backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs) which corresponds to the hedging pricing of European contingent claims. By introducing an auxiliary extended $\tilde{G}$-expectation space, we propose a class of $\theta$-schemes to discrete $G$-BSDEs in this space. With the help of nonlinear stochastic analysis techniques and numerical analysis tools, we prove that our schemes admit half-order convergence for approximating $G$-BSDE in the general case. In some special cases, our schemes can achieve a first-order convergence rate. Finally, we give an implementable numerical scheme for $G$-BSDEs based on Peng's central limit theorem and illustrate our convergence results with numerical examples.

30 pages, 2 figures

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Cited by in corpus (1)

• A monotone scheme for G-equations with application to the explicit convergence rate of robust central limit theorem