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 markets
  • entropy and financial value of information
  • optimal investment strategies in markets, with prices depending on the volume of trading
  • robust arbitrage and model-independent pricing
  • discrete time models and their continuous time limits in the presence of market imperfections
  • numerical methods for pricing financial derivatives
  • applications 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 manifolds
  • stochastic partial differential equations (especially stochastic Navier-Stokes and Euler equations arising in the context of turbulence phenomena)
  • stochastic analysis on Riemannian and Finslerian manifolds
  • rough 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.

We welcome PhD applications across a range of mathematical finance and stochastic analysis topics.