MCFG offers a thriving research environment and a critical mass which is rarely found in a single university. Most of the group members are leading experts in their area of mathematical/quantitative finance.
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, robust modelling, financial stability and financial big data.
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. In the area of big data, Ning Wang is working on sentiment analysis based on social media data, as well as on using data to establish metrics for learning and identification purposes and Terry Lyons is developing theory to link rough path theory with machine learning.
Doyne Farmer, who is a member of INET (the Institute for New Economic Thinking), is developing new dynamical systems, network and simulation-based approaches to understanding and forecasting financial stability.
In numerical methods for high-dimensional problems, 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, and Terry Lyons devised the cubature method for solving stochastic differential equations.
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.
Sam Cohen is also interested in questions of model robustness and its interaction with statistical modelling and optimal control. He also has more general interests in stochastic analysis, in particular the theory of backward SDEs. Michael Monoyios works on stochastic portfolio theory, optimal investment, valuation and hedging in incomplete markets, and on partial and inside information problems.
Álvaro Cartea works on algorithmic trading and in energy and commodity markets. Some of his work focuses on the mathematical models of algorithmic trading and also investigates the effect that computerised and high-frequency trading has on the quality of modern electronic exchanges.
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.
Within the Mathematical Institute, MCFG is closely affiliated with the Stochastic Analysis and Numerical Analysis groups, and also OCIAM, the Oxford Centre for Industrial and Applied Mathematics, enabling cross-fertilisation of ideas and techniques. In addition, through Oxford Finance, and OMI (Oxford-Man Institute of Quantitative Finance), the MCFG maintains strong ties with all other groups, institutes and departments within Oxford University with an interest in financial research, including the Statistics, Engineering Science, Computer Science and Economics departments, and the Said Business School.