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金融工程研究中心学术报告：SDE, BSDE under Nonlinear Expectation and the Paths of PDE
- 来源：
- 学校官网
- 收录时间：
- 2025-10-18 15:46:23
- 时间：
- 2025-07-16 09:40:00
- 地点：
- 苏州大学本部天元讲堂
- 报告人：
- 彭实戈
- 学校：
- -/-
- 关键词：
- SDE, BSDE, Nonlinear Expectation, PDE, G-Brownian motion, Financial Mathematics, Deep Learning
- 简介：
- In this talk we begin with (forward) stochastic differential equations (SDE, or FSDE) and backward stochastic differential equations (BSDE) driven by a standard d-dimensional Brownian motion defined on a probability space. The solution of the BSDE is in fact a path-solution of the corresponding (deterministic) quasilinear differential differential equations. This discovery, combined with the magic deep learning approach, provides a powerful tool of the numerical solution of a system of a high dimensional partial differential equation of parabolic and elliptic types. We also discuss the fully nonlinear case in which the Brownian motion is replaced by a d-dimensional G-Brownian motion under a nonlinear expectation space.
- -/- 58
报告介绍：
In this talk we begin with (forward) stochastic differential equations (SDE, or FSDE) and backward stochastic differential equations (BSDE) driven by a standard d-dimensional Brownian motion defined on a probability space. The solution of the BSDE is in fact a path-solution of the corresponding (deterministic) quasilinear differential differential equations. This discovery, combined with the magic deep learning approach, provides a powerful tool of the numerical solution of a system of a high dimensional partial differential equation of parabolic and elliptic types. We also discuss the fully nonlinear case in which the Brownian motion is replaced by a d-dimensional G-Brownian motion under a nonlinear expectation space.
报告人介绍：
彭实戈，中国科学院院士，山东大学教授，博士生导师山东大学泰山学堂院长，山东大学数学与交叉科学研究中心主任，2020未来科学大奖--数学与计算机科学奖获得者。1974年毕业于山东大学物理系，1986年获巴黎第九大学数学与自动控制三阶段博士学位和普鲁旺斯大学应用数学博士学位。主要研究方向为非线性期望与随机积分，倒向随机微分方程，随机控制和金融数学等。彭实戈院士创立的“倒向随机微分方程”(BSDE)在期权期货等金融衍生证券定价中有重要的作用，他也是中国金融数学的奠基人。2010年在印度海德拉巴召开的国际数学家大会上，彭实戈院士被邀请做了《倒向随机微分方程，非线性数学期望及其应用》大会报告。
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