Welcome...

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 Senior Research Fellow at New College.

My main research interests are in the areas of stochastic analysis and mathematical finance. In particular, I am interested in the interaction between statistical learning, decision making and control and uncertainty aversion.

One area I have been working on recently is how to build statistical uncertainty directly into preferences. This can be done using a "nonlinear expectation", which involves considering a range of possible probabilistic models, and combining them in a nonlinear way. By using observational data to determine which models are reasonable we connect our observations and our preferences in a direct way.

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.

For more details, see my papers. I also have interests in other areas of mathematics and statistics.

I am the author (with Robert Elliott) of the textbook Stochastic Calculus and Applications (2nd Ed.). Errata can be found here, and a preview is on Google books here.

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.

Beyond mathematics, I have interests in philosophy and Christian theology, and attend St Ebbes Church. Together with Paul Roberts I wrote a booklet on 'Being a christian in mathematics' an associated interview is here. In the past I also wrote a beer review blog here.