I am an Associate Professor in the Mathematical Institute at Oxford. I am also an associate member of the Oxford-Man Institute, a member of the Oxford-Nie Financial Big Data Lab and a College Lecturer at New College.
My main research interests are in the areas of stochastic analysis and mathematical finance. In particular, I work with Backward Stochastic Differential Equations (BSDEs), which arise in various areas in stochastic control and mathematical finance. I am interested in problems associated with decision making in the presence of risk and uncertainty.
A key problem in risk-averse decision making is time-consistency - "How can I be sure that tomorrow's decisions will satisfy today's objectives?" To guarantee time-consistency, we must ensure that the objective pursued satisfies certain properties. These properties, in general, are satisfied by solutions to "Backward Stochastic Differential Equations".
My doctoral work concerned Backward Stochastic Differential Equations in non-classical situations, namely where randomness can arise from processes other than a Brownian motion. I also considered the corresponding equations in discrete time. At the moment my work concerns various extensions of these equations to allow for different forms of uncertainty, and for possible forms of time-inconsistency.
For more details, see my papers. I also have interests in other areas of mathematics and statistics.
My PhD was at the University of Adelaide, under the supervision of Robert Elliott and the late Charles Pearce. I also completed my undergraduate and honours studies at the University of Adelaide, again under the supervision of Charles Pearce.Along with Gechun Liang and Arnaud Lionnet, I organised the meeting `BSDEs, Numerics and Finance'.
Sadly I am unable to supervise students for summer internships at the present time.