Our research interests span a broad range of topics in continuous and discrete time.In mathematical finance our areas of research activity include:arbitrage and option pricing in markets with friction and incomplete marketsentropy and financial value of informationoptimal investment strategies in markets, with prices depending on the volume of tradingrobust arbitrage and model-independent pricingdiscrete time models and their continuous time limits in the presence of market imperfectionsnumerical methods for pricing financial derivativesapplications of optimal stopping, singular control, and game theory to investment problems in the real economy ("real options").In stochastic analysis our research focuses on:infinite dimensional stochastic analysis, including stochastic differential equations on infinite dimensional manifoldsstochastic partial differential equations (especially stochastic Navier-Stokes and Euler equations arising in the context of turbulence phenomena)stochastic analysis on Riemannian and Finslerian manifoldsrough paths and their applications to modelling probabilistic phenomena and numerical analysis (for example non-linear filtering)Feynman path integrals and more broad applications to mathematical physics, biology and finance.