Dr Arnaud Lionnet is a Lecturer in Mathematical Statistics. Broadly speaking, he works in probability, numerical methods and mathematical finance and economics.
One topic he has been fairly involved with is the theoretical and numerical analysis of Backward Stochastic Differential Equations (BSDEs). These equations provide, among other applications, a probabilistic reformulation of parabolic Partial Differential Equations (PDEs). As a result, he became interested more generally in probabilistic numerical methods for PDEs.
Dr Lionnet recently started working on a very different research topic: systemic risk in financial networks. This is the risk specifically associated with the fact that the financial system is made of a large number of interconnected financial institutions. As a result, a moderate economic shock can trigger a large-scale epidemic of bankruptcies, by domino effect.
More generally, he is increasingly interested in statistical learning and in economics.