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

                發布者:文明辦作者:發布時間:2022-06-16瀏覽次數:10


                主講人:徐承龍 上海財經大學教授


                時間:gogo体育官网6月17日16:00


                地點:騰訊會議 210 222 202


                舉辦單位:數理學院


                主講人介紹:徐承龍,教授,博士生導師。兼任上海市教委科一名之恩學計算E-研究院特聘研究想法員,中國管理科學研究院智能投顧實驗室特聘研究員, 北京大學出版社《智能投顧前ω瞻》系列叢書編委,科學出热血变得沸腾版社《金融數學》系列叢書編委。 至今發表「論文70余篇,教材(專著)6本。主講課程《金融中的模型與計算》,《金融隨機分析》,《固定收异能益證券與隨機利率模型》等。曾獲得上海市優秀教材獎(2015年),上海市優秀教學成果一等〒獎(2009年),寶鋼優秀教師≡獎(2009年度),第一批國家級精品补充说道資源共享課《金融衍生物定價理論》負責人(2016年6月批準)。


                內容介紹: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.

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