Ben graduated from the University of Bristol in 2015 with an MSc in Mathematics. He completed a final project on the Markov Chain Central Limit Theorem and his main interests are in probability theory and applications. Outside of maths, Ben has worked in online marketing and analytics for an adventure travel company and he enjoys running, walking, singing and reading.

Research project title:
Topics in optimal stopping and optimal transport

Supervisor(s):
Alex Cox

Project description:
Ben studied various stochastic optimisation problems and the connections between them. Recent work on optimal stopping problems has investigated imposing a constraint on the expected value of the stopping time in these problems to obtain so-called constrained optimal stopping problems. Ben built on this work, making use of a connection to stochastic optimal control problems. This approach required developing an understanding of the modern theory of stochastic optimal control, including the theory of weak solutions to partial differential equations in the viscosity sense. Certain problems of this type can be represented in terms of Monge-Ampère equations, a highly non-linear class of PDEs, which arise in the classical Monge Kantorovich optimal transport problem. Ben was interested in this problem, as well as the variation, martingale optimal transport, in which additional constraints are imposed. Methods of martingale optimal transport have also been used in the Skorokhod embedding problem, a classical problem in probability theory. Each of these classes of problems has a financial motivation. Ben was particularly interested in how these problems are related.