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").

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.

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