PhD in Mathematics - Mathematical Finance and Stochastic Analysis in York United Kingdom | University of York

Our research covers diverse topics in both continuous and discrete time frameworks.
Within mathematical finance, we investigate:
arbitrage opportunities and option valuation in imperfect and incomplete markets
the role of entropy and information's financial impact
optimal trading approaches in volume-sensitive markets
model-free arbitrage and pricing without specific assumptions
discrete models converging to continuous limits under market constraints
computational techniques for derivative pricing
real-world investment applications using optimal stopping, singular control, and game theory (real options).
In stochastic analysis, we concentrate on:
infinite-dimensional stochastic processes, including manifold-based differential equations
stochastic PDEs (particularly turbulence-related Navier-Stokes and Euler equations)
stochastic methods on Riemannian and Finslerian geometries
rough path theory with applications to probabilistic modeling and numerical methods (e.g., non-linear filtering)
Feynman path integrals and their interdisciplinary applications in physics, biology, and finance.