关于随机微分方程Girsanov变换的路径独立性

On path independence of Girsanov transformation for stochastic differential equations

本文介绍了近十年来关于随机微分方程Girsanov变换的路径独立性的主要研究成果.该性质因反映了金融数学中市场的有效性而具有明确的应用背景,也因等价于一些非线性偏微分方程而具有数学研究价值.本文分别就经典的随机微分方程、带跳的随机微分方程、随机偏微分方程和分布依赖随机微分方程,介绍Girsanov变换的路径独立性所联系的非线性偏微分方程,并对其他相关研究加以评注.最后,作为一个新结果,本文使用非线性偏微分方程刻画了随机微分方程解的路径无关性.

In this paper,we introduce results obtained over the past ten years on the path-independence of the Girsanov transformation for stochastic differential equations,which was originated in 1990s from an important market efficiency property in mathematical finance studies.We end up the paper with a new result characterizing the solution of stochastic differential equations using nonlinear partial differential equations.