标题： 二维G-热方程的数值方法 显示英文标题

标题： Numerical methods for two-dimensional G-heat equation

摘要： G-期望是一种次线性期望。 由于其处理模型不确定性能力，它是金融产品定价和风险管理的重要工具。 问题在于如何有效地量化它，因为常用的蒙特卡洛方法不起作用。 幸运的是，G-正态随机变量的期望可以与完全非线性G-热方程的粘性解联系起来。 本文提出了一种新的二维G-热方程数值格式，并更多地关注存在相关性不确定性的案例，特别是当相关性从负到正变化时的案例。 该格式是单调的、稳定的并且收敛的。 数值测试表明该格式非常高效。 显示英文摘要

摘要： The G-expectation is a sublinear expectation. It is an important tool for pricing financial products and managing risk thanks to its ability to deal with model uncertainty. The problem is how to efficiently quantify it since the commonly used Monte Carlo method does not work. Fortunately, the expectation of a G-normal random variable can be linked to the viscosity solution of a fully nonlinear G-heat equation. In this paper, we propose a novel numerical scheme for the two-dimensional G-heat equation and pay more attention to the case that there exists uncertainty on the correlationship, especially to the case that the correlationship ranges from negative to positive. The scheme is monotonic, stable, and convergent. The numerical tests show that the scheme is highly efficient.