Research in Mathematical & Computational Finance

The Oxford Mathematical and Computational Finance Group is one of the leading academic research groups  in the world focused on mathematical modeling in finance and offers a thriving research environment, with experts covering multiple  areas of quantitative finance. Our group maintains close links with the Data Science, Stochastic Analysis and Numerical Analysis groups as well as the Institute for New Economic Thinking (INET) and the Oxford Probability Group,  enabling cross-fertilisation of ideas and techniques.

Research activities of the group cover a wide spectrum of topics in Quantitative Finance, ranging from  market microstructure and high-frequency modeling  to macro-financial modeling and systemic risk, as well as more traditional topics such as  portfolio optimisation, derivative pricing, credit risk modeling, using a variety of methods: stochastic analysis, probability, partial differential equations, optimisation, numerical simulation, statistics and machine learning.

Mathematical Foundations and Continuous-time finance

Positioned within Oxford's Mathematical Institute, the group has developed a unique expertise in the mathematical foundations underlying quantitative finance and pioneered new approaches in mathematical modeling.

Anna AnanovaSam Cohen, Rama Cont, Ben HamblyJan Obloj, David Proemel and Zhongmin Qian explore topics in stochastic analysis  -stochastic calculus, backward stochastic differential equations, interacting particle systems, Malliavin calculus, Functional Ito calculus, rough path theory, pathwise methods in stochastic analysis, optimal transport- and their applications to the design of robust models for the pricing and hedging of derivatives in presence of model uncertainty.
Michael Monoyios works on stochastic portfolio theory, optimal investment, valuation and hedging in incomplete markets, and models with information asymmetry in continuous time.

Statistical modeling and Machine Learning in Finance

Our group is one of the few academic research teams in the world with an active research agenda at the interface of machine learning and quantitative finance.
Hanqing Jin is Director of the Oxford-Nie Big Data Lab, where Ning Wang has developed algorithms for sentiment analysis based on social media data.
Sam Cohen is  interested in model robustness and its interaction with statistical modelling and optimal control.
Rama Cont investigates the use of Deep Learning and  data-driven modelling for the design, simulation and monitoring   of high frequency trading strategies.
Terry Lyons and his team investigate the use of rough path signatures for machine learning.

Market microstructure and algorithmic finance

Álvaro Cartea  focuses on mathematical models of algorithmic trading and  the design of optimal trade execition strategies in electronic markets.

Rama Cont pioneered the analytical study of stochastic models for limit order books and intraday market modeling, and investigates the impact of algorithmic trading on market stability and liquidity.

Doyne Farmer has made fundamental contributions to  empirical market microstructure, price impact modeling and the modeling of intraday market behaviour as an evolutionary system.

Macro-financial modeling: financial stability and systemic risk

Our group is actively engaged in the development of mathematical models of large-scale financial systems with the goal of providing quantitative insights on financial stability and systemic risk to regulators and policy makers.
Rama Cont and Ben Hambly  investigate the link between micro- and macro-behavior in stochastic models of direct and indirect contagion in financial markets, using network models and analogies with interacting particle systems.

Rama Cont and Doyne Farmer, both Senior Research Fellows at the  Institute for New Economic Thinking (INET), developed network model and simulation-based approaches for macro stress-testing and monitoring systemic risk in banking systems, in liaison with central banks and international organisations such as the Bank of England, the European Central Bank, IMF and Norges Bank.

Computational Finance

Our group is a leader in the development of novel numerical methods for high-dimensional problems in finance:
Mike Giles is a leading expert on multilevel Monte-Carlo methods and their applications in finance;
Raphael Hauser has developed robust numerical methods for portfolio optimisation and high-dimensional optimisation problems in finance;
Christoph Reisinger develops novel and efficient numerical methods for stochastic control problems and high-dimensional (S)PDEs and their applications in finance;
Terry Lyons devised cubature methods in Wiener space for solving stochastic differential equations.

Sam Howison and Jeff Dewynne were among the pioneers in the development of advanced  partial differential equation methods in finance, the use of asymptotic methods for their solution and their application to various markets such as energy and commodities.

Behavioural finance

Hanqing Jin  develops quantitative models of investor behaviour, building on the fundamental work of Kahneman and Tversky's prospect theory and Lopes' SP/A theory. 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.
Doyne Farmer develops agent-based models of  financial markets and economic systems for market design and policy analysis.

 

For more information on research activities of our group please visit the individual websites of group members.