报告题目：Characterising the path-independence of stochastic differential equations: a problem arising in financial modelling

报告时间：2019年12月24日（星期二）下午15：00-16:00

报告地点：数学楼2-3会议室

报告摘要:

This talk will address a problem arising in financial modelling with stochastic differential equations (SDEs). A characterisation theorem will be derived in which we establish a new link from SDEs to nonlinear parabolic PDEs. Starting from the necessary and sufficient

conditions of the path-independence of the density of Girsanov transform for SDEs, we are able to derive a characterisation by means of nonlinear parabolic equations of Burgers-KPZ type. Extensions to the cases of degenerated SDEs, jump SDEs, as well as to (infinite dimensional) SDEs on separable Hilbert spaces will be discussed. A perspective to stochastically deformed dynamical systems will be briefly considered.

报告人简介：

现任职于英国斯旺西大学，是江苏师范大学双聘教授、华中科技大学数学中心东湖讲座教授。在 《Stochastic Processes and their Applications》、 《Journal of Functional Analysis》、 《Journal ofDifferential Equations》等国际知名期刊上发表学术论文90多篇。其研究领域包括：随机分析、非标准分析和无穷维分析；研究问题包括：数理金融、数学物理、特殊结构量子场和统计力学等学科中与概率论相关的无穷维分析问题。