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

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。

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.