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

本项目的中心目标是克服解耦的正反向随机微分方程和半线性偏微分方程数值逼近中的维数诅咒。介绍并分析了基于多级皮卡德近似的新逼近方法。特别是，这些近似方法对于金融行业的一揽子期权定价至关重要。

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.