Numerical methods for high dimensional problems

Partial differential equations (PDEs) are universal tools in modeling and occur in financial engineering in derivatives pricing, portfolio selection, risk management, optimal transport, etc. When taking into account realistic features of the market, PDEs often arise as complex nonlinear problems, and often in very high dimension. Their numerical resolution is a long standing challenge in applied mathematics, and the last years have seen a breakthrough with the input of machine learning and multi-level Monte-Carlo techniques. Our research investigates in particular the challenging case of fully nonlinear PDEs, and develops new robust machine learning schemes.