“北京大学数量经济与数理金融教育部重点实验室”学术报告——On the path-independent property for stochastic differential equations: a problem arising in financial modeling
主 题: “北京大学数量经济与数理金融教育部重点实验室”学术报告——On the path-independent property for stochastic differential equations: a problem arising in financial modeling
报告人: Prof. Jiang-Lun Wu (Swansea University, UK)
时 间: 2018-01-11 14:00-15:00
地 点: Room 1560, Sciences Building No. 1
Abstract: This talk will address a problem arising in financial modeling with stochastic differential equations (SDEs). A characterization 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 characterization 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.
Bio: Jiang-Lun Wu is a professor of Mathematics at Swansea University. He obtained his PhD from Institute of Applied Mathematics, Chinese Academy of Sciences, under the supervision of Academician Jia-An Yan. He was A v Humboldt research fellow at Ruhr University Bochum, Germany. His research focuses mainly on stochastic analysis, partial differential equations, statistical physics and financial mathematics.