Solving non-linear Kolmogorov equations in large dimensions by using deep learning: a numerical comparison of discretization schemes

Understand

Non-linear partial differential Kolmogorov equations are successfully used to describe a wide range of time dependent phenomena, in natural sciences, engineering or even finance.

• For example, in physical systems, the Allen-Cahn equation describes pattern formation associated to phase transitions.
• In finance, instead, the Black-Scholes equation describes the evolution of the price of derivative investment instruments.
• Such modern applications often require to solve these equations in high-dimensional regimes in which classical approaches are ineffective.