Gaussian Kernel Regression Method for PDE's with Random Coefficients Based On the F-K Formula

主讲人：徐承龙 上海财经大学教授

时间：2022年6月17日16：00

地点：腾讯会议 210 222 202

举办单位：数理学院

主讲人介绍：徐承龙，教授，博士生导师。兼任上海市教委科学计算E-研究院特聘研究员，中国管理科学研究院智能投顾实验室特聘研究员, 北京大学出版社《智能投顾前瞻》系列丛书编委，科学出版社《金融数学》系列丛书编委。 至今发表论文70余篇，教材（专著）6本。主讲课程《金融中的模型与计算》，《金融随机分析》,《固定收益证券与随机利率模型》等。曾获得上海市优秀教材奖（2015年），上海市优秀教学成果一等奖（2009年），宝钢优秀教师奖（2009年度），第一批国家级精品资源共享课《金融衍生物定价理论》负责人(2016年6月批准)。

内容介绍：This paper presents a Gaussian kernel regression method for solving the PDE's with random coefficients in high dimension based on the Feynman-Kac formula and the Monte Carlo simulations. Firstly, a new adaptive step size Euler discretization scheme is presented, which is suitable for solving the stochastic differential equation governing the PDE's containing random coefficients. Numerical experiments show the robustness and efficiency of the scheme. Secondly, a semi-stochastic sampling method in the product space is proposed for the preparation of simulations. Third, a Gaussian kernel regression method is applied for solving the probability density function of the solution to the PDE's with random coefficients, by mean of the Feynman-Kac formula and the Monte Carlo simulation processes, which generate samples for regression. Numerical experiments show the efficiency and convergence of the proposed method for a model problem in high-dimensional domain.