Research
MCFG offers a thriving research environment and a critical mass rarely to be found in a single university. Most of the group members are leading experts in the area of mathematical/quantitative finance, and have been or are on the editorial boards of top scholarly journals such as Annals of Applied Probability, Finance and Stochastics, Mathematical Finance, Applied Mathematical Finance, Operations Research, SIAM Journal on Control and Optimization, and SIAM Journal on Financial Mathematics.
MCFG's research covers a wide spectrum of problems in Mathematical Finance, ranging from portfolio selection, derivative pricing, credit and convertibles, to market microstructure models. In particular, recently there has been great interest in mathematical aspects of economic fundamentals, particularly behavioural finance and the theory of dynamic risk preferences, which represent some of the most exciting new directions and developments in the mathematical finance area. Hanqing Jin and Xunyu Zhou have been developing a mathematical behavioural finance theory, building on the fundamental work of Kahneman and Tversky's prospect theory and Lopes' SP/A theory. Vicky Henderson and Zuoquan Xu are working on optimal stopping problems with behavioural criteria. Thaleia Zariphopoulou has made significant contributions to forward utility theory. Her arrival brings expertise to add to that of Dmitry Kramkov, Michael Monoyios and Vicky Henderson.
Another particular strength of MCFG is numerical methods, especially for high-dimensional problems, where Mike Giles is breaking new ground in multilevel Monte-Carlo methods, Christoph Reisinger develops novel and efficient numerical methods for high-dimensional PDEs with application to option pricing, Raphael Hauser specialises on cutting-edge methods for robust optimisation, and Terry Lyons (the Wallis Professor of Mathematics) devised the cubature method for solving stochastic differential equations.
Stochastic analysis is another strength of the group. Ben Hambly, Jan Obloj and Zhongmin Qian are experts in stochastic analysis, whose work uses the latest results from that field to study backward stochastic differential equations, formulate and solve derivatives pricing models, and investigate model uncertainty and robustness. Finally, Sam Howison and Jeff Dewynne focus on models in various markets such as energy and commodities, and on asymptotic methods for their solution. Please visit the individual websites of group members for more details about what we are up to.
The flagship of the MCFG is the Nomura Centre for Mathematical Finance, which was established in 2001 with the support of the Nomura Group, with the aim of promoting research in mathematics and finance and a special emphasis on approaches that combine practical relevance with mathematical interest. Part of Oxford University's Mathematical Institute, the MCFG is closely affiliated with OCIAM, the Oxford Centre for Industrial and Applied Mathematics, enabling cross-fertilisation of ideas and techniques. In addition, through the Oxford Financial Research Centre (OFRC), and lately the Oxford-Man Institute of Quantitative Finance (OMI), the MCFG maintains strong ties with all other groups, institutes and departments within Oxford University with an interest in financial research, including the Statistics, Physics, Computer Science and Economics departments, and the Said Business School.