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), the Oxford-Man Institute of Quantitative Finance 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 Ananova, Sam Cohen, Rama Cont, Ben Hambly, Jan Obloj 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.
Jan Obloj works on robust formulations of classical problems -- pricing, hedging, risk management, optimal investment – and seeks to understand and quantify the effects of model uncertainty.
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. Several group members are Fellows of the Alan Turing Institute.
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 exploring applications of Deep Learning to continuous-time finance as well as issues related to model robustness and its interaction with statistical modelling and optimal control.
Rama Cont and Justin Sirignano investigate the use of Deep Learning and data-driven modelling in finance.
Terry Lyons and his team investigate the use of rough path signatures for machine learning.
Jan Obloj employs tools from the optimal transport theory to develop data-driven estimators for risk measures.
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 Research Fellows at the Institute for New Economic Thinking (INET), have developed network models 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.
Rama Cont is Director of the Oxford Martin Programme on Systemic Resilience, an interdisciplinary programme aimed at exploring solutions for managing stress scenarios with the potential for major and prolonged economic disruption, severe human or economic impacts, and contagion.
Our group is a leader in the development of advanced numerical methods and high performance computiing for high-dimensional problems in finance:
Mike Giles is a pioneer on multilevel Monte-Carlo methods and their applications in finance, and a leading expert on the use of GPU and high performance computing methods in finance.
Raphael Hauser has developed robust numerical methods for portfolio optimisation and high-dimensional optimisation problems in finance.
Jan Obloj develops numerical methods for martingale optimal transport problems which yield bounds for option prices and optimal transport techniques for model calibration.
Justin Sirignano has pioneered the use of Deep Learning methods for various applications in finance ranging from credit risk modeling to limit order book modeling.
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.
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.
Jan Obloj works on optimal decision problems for cumulative prospect theory agents and understanding their actions in dynamic environments, such as casino gambling.
For more information on research activities of our group please visit the individual websites of group members.