Peter graduated in 2024 from the University of Warwick with a master’s in Mathematics and Computer Science. He focussed on analysis and probability, with his dissertation on numerical methods for stochastic differential equations and their applications to options pricing. A more recent interest is the theory of rough paths and the links with stochastic analysis.

Outside of maths, Peter enjoys playing the piano and sampling the many real ales/ciders from across the country.

Research project title:
Stochastic Optimal Control with Singularities: Theory, Numerics, and Applications

Supervisor(s):
Avi Mayorcas

Project description:
In this project, we study stochastic optimal control problems through the lens of forward–backward stochastic differential equations (FBSDEs). A key motivation comes from economics, where individual wealth and consumption are often modelled using singular utility functions such as CRRA. These singularities fall outside the usual assumptions of Lipschitz continuity that underpin current convergence guarantees for numerical methods such as DeepBSDE. One of the central aims is to establish new theoretical results on existence, uniqueness, and (numerical) convergence of FBSDE systems in these more singular settings.

Beyond the individual case, we also investigate mean field models, where the objective functional depends on the law of the state process and interactions occur at the population level. This extension connects naturally to problems in economics and finance, but also to broader applications where individual behaviour is influenced by collective dynamics. By combining rigorous mathematical analysis with modern machine learning methods, the project seeks to both advance the theoretical understanding of singular control problems and provide practical numerical tools for solving them.