This talk reviews recent developments in the regularity analysis and the numerical approximation of nonlinear stochastic differential equations (SDEs) and their associated deterministic second-order linear Kolmogorov partial differential equations (PDEs). Nonlinear SDEs appear, for example, in fundamental models from financial engineering, neurobiology and quantum field theory. In particular, we outline in this talk how nonlinear SEEs are day after day used in the financial engineering industry to estimate prices of financial derivatives. The nonlinearities in the SDEs from applications often fail to be globally Lipschitz continuous. A key topic of this talk is therefore the regularity analysis and the numerical approximation of SDEs with non-globally Lipschitz continuous nonlinearities.

Referent: Prof. Dr. Arnulf Jentzen, ETM Zürich