Numerical simulations for <i>G</i>-Brownian motion

doi:10.1007/s11464-016-0504-9

Front. Math. China

2016, Vol. 11

Issue (6) : 1625-1643 https://doi.org/10.1007/s11464-016-0504-9

RESEARCH ARTICLE

Numerical simulations for G-Brownian motion

Jie YANG,Weidong ZHAO(

)

School of Mathematics & Finance Institute, Shandong University, Jinan 250100, China

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Abstract

This paper is concerned with numerical simulations for the GBrownian motion (defined by S. Peng in Stochastic Analysis and Applications, 2007, 541–567). By the definition of the G-normal distribution, we first show that the G-Brownian motions can be simulated by solving a certain kind of Hamilton-Jacobi-Bellman (HJB) equations. Then, some finite difference methods are designed for the corresponding HJB equations. Numerical simulation results of the G-normal distribution, the G-Brownian motion, and the corresponding quadratic variation process are provided, which characterize basic properties of the G-Brownian motion. We believe that the algorithms in this work serve as a fundamental tool for future studies, e.g., for solving stochastic differential equations (SDEs)/stochastic partial differential equations (SPDEs) driven by the G-Brownian motions.

Keywords Nonlinear expectation G-Brownian motion G-normal distribution Hamilton-Jacobi-Bellman (HJB) equation

Corresponding Author(s): Weidong ZHAO

Issue Date: 18 October 2016

Cite this article:

Jie YANG,Weidong ZHAO. Numerical simulations for G-Brownian motion[J]. Front. Math. China, 2016, 11(6): 1625-1643.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-016-0504-9
https://academic.hep.com.cn/fmc/EN/Y2016/V11/I6/1625

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