在随机分析中，我们的研究重点是无限维随机分析
Our research interests span a broad range of topics in continuous and discrete time.<br>In mathematical finance our areas of research activity include:<br>arbitrage and option pricing in markets with friction and incomplete markets<br>entropy and financial value of information<br>optimal investment strategies in markets, with prices depending on the volume of trading<br>robust arbitrage and model-independent pricing<br>discrete time models and their continuous time limits in the presence of market imperfections<br>numerical methods for pricing financial derivatives<br>applications of optimal stopping, singular control, and game theory to investment problems in the real economy (real options).<br>In stochastic analysis our research focuses on:<br>infinite dimensional stochastic analysis, including stochastic differential equations on infinite dimensional manifolds<br>stochastic partial differential equations (especially stochastic Navier-Stokes and Euler equations arising in the context of turbulence phenomena)<br>stochastic analysis on Riemannian and Finslerian manifolds<br>rough paths and their applications to modelling probabilistic phenomena and numerical analysis (for example non-linear filtering)<br>Feynman path integrals and more broad applications to mathematical physics, biology and finance.