On numerical approximations of high-dimensional nonlinear parabolic partial differential equations and of backward stochastic differential equations

高维非线性抛物型偏微分方程和倒向随机微分方程的数值逼近

• 批准号: 381158774
• 负责人: Professor Dr. Martin Hutzenthaler
• 金额: --
• 依托单位: Arbeitsgruppe Stochastische Analysis
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2017
• 资助国家: 德国
• 起止时间: 2016-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/381158774?language=en
• 关键词: numerical; approximations; dimensional; nonlinear; parabolic

The central goal of this project is to overcome the curse of dimensionality in the numerical approximation of decoupled forward-backward stochastic differential equations and semilinear partial differential equations. We introduce and analyze new approximation methods which are based on multilevel Picard approximations from the first project phase. In particular, these approximation methods are essential for pricing basket options in the financial industry.

这个项目的中心目标是克服在解耦的正倒向随机微分方程和半线性偏微分方程的数值逼近维数灾难。我们介绍和分析新的近似方法，这是基于多层次的皮卡近似从第一个项目阶段。特别是，这些近似方法是必不可少的定价在金融行业的篮子期权。