Working title: Applications of machine learning to financial risk management

The project aims to apply machine learning methods to problems within finance. With the advent of increased computational capacity and access to ever increasing volumes of data, machine learning methods have begun to make significant impact on the domain of quantitative finance, enabling traders and risk managers to solve previously intractable problems, and automate routine tasks at large scale. As applications of machine learning increase, we are equally faced with the a number of open problems which may be amenable to these methods, and further, the use of deep learning methods in particular introduces questions regarding the explainability, robustness and efficiency of algorithms. This project falls within the EPSRC Mathematical Sciences research area.
The overarching aim of this PhD project is to develop novel machine learning methodology with a view to applying it in derivatives pricing and hedging. A common problem faced in finance is that of managing risk through the construction of a portfolio of hedging instruments. Modern quantitative finance has equipped the trader with an effective toolkit in which to optimally construct such a portfolio, under the idealised assumptions of complete markets and zero market frictions. When these assumptions do not hold, the classical methods may break down, prompting researchers to investigate model-free hedging through methods such as deep reinforcement learning.
A major limitation of these new approaches is the availability of real market data on which to train the algorithms. It is well known that neural networks require vast quantities of training data in order to reach global optima, but in the case of over-the-counter derivatives, the amount of useful real-life data available is limited. For example, over a ten-year period, with daily data, we would arrive at only a few thousand samples on which to train our models.
This limitation motivates the need for an effective market simulator, through which we may generate training data for our hedging agent. Of course, classical quantitative finance has a wide array of parametric models for markets, such as continuous time semi-martingale models, local volatility models, and stochastic volatility models. However, these models are notoriously difficult to fit to real-world data and rely on significant modelling assumptions, so that a deep hedging agent trained on these paths is likely to perform poorly when put into live trading on real world data. Instead, there has been some interest in model-free simulation of markets using generative machine learning methods, and some progress has been made into market simulation using neural networks.
However, there are some issues with the current state-of-the-art market generators, when used to train the hedging agent. In particular, the paths generated exhibit drifts which permit the trading agent to find statistical arbitrage strategies - ones which on average produce a positive payoff - rather than performing proper risk management through hedging. Thus, a focus for this PhD project is to investigate methods which can be applied to remove statistical arbitrage from the market generator and better account for uncertainty about the future state of markets.
The outcomes for this project will be new methodologies for managing financial risk that rely less on assumptions and specific models, than current methods. Therefore, they will be more robust and resilient to changing states of the world in the future.
This project is being undertaken in collaboration with JPMorgan Chase Bank, where I have been working on a part-time, one day per week basis, since February 2020.

The primary CDT impact will be training 75 PhD graduates as the next generation of leaders in statistics and statistical machine learning. These graduates will lead in industry, government, health care, and academic research. They will bridge the gap between academia and industry, resulting in significant knowledge transfer to both established and start-up companies. Because this cohort will also learn to mentor other researchers, the CDT will ultimately address a UK-wide skills gap. The students will also be crucial in keeping the UK at the forefront of methodological research in statistics and machine learning.
After graduating, students will act as multipliers, educating others in advanced methodology throughout their career. There are a range of further impacts:
- The CDT has a large number of high calibre external partners in government, health care, industry and science. These partnerships will catalyse immediate knowledge transfer, bringing cutting edge methodology to a large number of areas. Knowledge transfer will also be achieved through internships/placements of our students with users of statistics and machine learning.
- Our Women in Mathematics and Statistics summer programme is aimed at students who could go on to apply for a PhD. This programme will inspire the next generation of statisticians and also provide excellent leadership training for the CDT students.
- The students will develop new methodology and theory in the domains of statistics and statistical machine learning. It will be relevant research, addressing the key questions behind real world problems. The research will be published in the best possible statistics journals and machine learning conferences and will be made available online. To maximize reproducibility and replicability, source code and replication files will be made available as open source software or, when relevant to an industrial collaboration, held as a patent or software copyright.