Robust analysis of multivariate extreme events
This research project is in competition for funding with one or more projects available across the EPSRC Doctoral Training Partnership (DTP). Usually the projects which receive the best applicants will be awarded the funding. Find out more information about the DTP and how to apply.
Application deadline: 15 March 2019
Start date: 1 October 2019
This project is to develop robust statistical techniques by leveraging knowledge in extremal integral representations, stochastic geometry and combining it with cutting-edge approaches from the now rapidly growing field of distributionally robust optimisation.
Being well-informed about the likely nature of future risks is of utmost importance to build a resilient infrastructure through adaptation. Specifically, in finance, many decisions involve the quantitative assessment of a large number of risk factors. To give an example, insurance companies routinely deliver estimates of 1/200 year value-at-risk for 3000 member portfolios with less than 20 years of history. What inherently exacerbates such tasks is:
- the short data history with extreme losses being scarce, and
- the large number of risk factors with potentially severe interdependencies at extreme levels.
While classically, one would assume an underlying measure to exploit the rich structure of joint extremes, it is practically almost impossible to estimate it in a high-dimensional setting and we also need to hedge against the uncertainty in the complex structure of interdependencies.
The latter is the goal of this project by means of a novel approach making use of fundamental stochastic dominance relationships, of which the main supervisor Dr Kirstin Strokorb is an expert and which triggered a scientific exchange with the additional co-supervisor Professor Stilian Stoev. Specifically, we propose to develop robust statistical techniques by leveraging knowledge in extremal integral representations, stochastic geometry and combining it with cutting-edge approaches from the now rapidly growing field of distributionally robust optimisation. Professor Anatoly Zhigljavsky completes the team through his expertise in stochastic optimisation.
Project aims and methods
While we assume a holistic approach for tackling the arising practical problems, the studentship will stick to a well-structured learning approach, starting to develop theory and methods first in lower-dimensional settings. As you are developing key skills, we aim to extend the research to higher dimensions.
This studentship will:
- extend the preliminary results of Dr Kirstin Strokorb and Professor Stilian Stoev guided by practical needs of regulatory bodies and in the insurance industry
- analyse the arising optimisation problems and propose suitable analytical and numerical techniques
- develop software for end users.
This project belongs to the young and thriving research direction of combining expert knowledge in extreme value theory (EVT) with techniques of distributionally robust optimisation (DRO). You will therefore conduct innovative research across disciplinary boundaries, in which regard Dr Kirstin Strokorb and Professor Anotoly Zhigljavsky will manage the majority of the student's time with regular theoretical feedback from Professor Stilian Stoev and practical advice from Professor Chen Zhou and Dr Robert Yuen.
By undertaking both theoretical and applied statistical research, playing an integral role in an international research team, and developing software to implement and disseminate research methods, you will develop multiple skills enabling you to work successfully in various environments.
This includes quantitative, analytic and modelling skills along the lines of DRO and EVT, critical thinking, development of growing independence in learning and research, time management as well as important oral and written communication skills at research level. Specifically, as you will be directly supported with expertise from finance and insurance, you will also learn how to translate ideas between economics and mathematics.
Finally, the project allows for an element of flexibility in that you, depending on their background and preferences, may put a stronger weight on either theoretical or practical advancements with growing complexity.