Mathematical Finance and Stochastic Analysis

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.

Mathematical Finance and Stochastic Analysis Seminar

Members

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