主講人：徐承龍 上海財(cái)經(jīng)大學(xué)教授

時(shí)間：2022年6月17日16：00

地點(diǎn)：騰訊會(huì)議 210 222 202

舉辦單位：數(shù)理學(xué)院

主講人介紹：徐承龍，教授，博士生導(dǎo)師。兼任上海市教委科學(xué)計(jì)算E-研究院特聘研究員，中國(guó)管理科學(xué)研究院智能投顧實(shí)驗(yàn)室特聘研究員, 北京大學(xué)出版社《智能投顧前瞻》系列叢書(shū)編委，科學(xué)出版社《金融數(shù)學(xué)》系列叢書(shū)編委。 至今發(fā)表論文70余篇，教材（專(zhuān)著）6本。主講課程《金融中的模型與計(jì)算》，《金融隨機(jī)分析》,《固定收益證券與隨機(jī)利率模型》等。曾獲得上海市優(yōu)秀教材獎(jiǎng)（2015年），上海市優(yōu)秀教學(xué)成果一等獎(jiǎng)（2009年），寶鋼優(yōu)秀教師獎(jiǎng)（2009年度），第一批國(guó)家級(jí)精品資源共享課《金融衍生物定價(jià)理論》負(fù)責(zé)人(2016年6月批準(zhǔn))。

內(nèi)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.