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.
We run regular seminars and host talks by external speakers from the UK and overseas, covering a wide range of topics of current interest in stochastic analysis and mathematical finance.
Push the boundaries of knowledge in our supportive and stimulating environment.