Mathematical finance and stochastic analysis

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").
• dynamic adverse selection and dynamic moral hazard problems in corporate finance, in particular, use of derivative instruments to reduce the welfare loss due to agency problems.

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.