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 (e.g. non-linear filtering)
- Feynman path integrals and more broadly applications to mathematical physics, biology and finance

Our research interests in mathematical finance span a broad range of topics in continuous and discrete time. 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

We run a weekly seminar hosting talks by external speakers from the UK and overseas covering a wide range of topics of current interest in stochastic analysis and mathematical finance.

Members of our group have authored a number of text books.

- Prof Zdzislaw Brzezniak
- Dr Alexei Daletskii
- Dr Boda Kang
- Dr Christian Litterer
- Dr Alet Roux
- Prof Tomasz Zastawniak
- Prof Alexander McNeil (York Management School)

*Photo: soupautomat4 by fdecomite, licensed under CC BY 2.0*