My research lies in the area of stochastic modelling and computation, and, more recently, the mathematical foundations of machine learning. It has made contributions to stochastic control and the numerical analysis of associated nonlinear PDEs, the mathematical foundations of reinforcement learning and deep learning, and computational finance.

I am always keen on interesting collaborations and PhD projects in the following and other areas.

Current research areas:

• Approximation and reinforcement learning of stochastic control problems, eg, policy gradient methods, numerical analysis of HJB equations.
• Mathematical analysis of artificial neural networks -- and real ones.
• Mean-field limits of particle systems and mean-field control problems.
• Numerical approximation of high-dimensional SDEs and PDEs.
• Simulation of SPDEs of Zakai-type and of large particle systems.
• Mathematical modelling of financial markets, eg, calibration, pricing and risk management of financial derivatives.

See the publications page to get an idea of the flavour of ongoing and past projects.