Robust analysis of multivariate extreme events

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
(i) the short data history with extreme losses being scarce and
(ii) 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.

In addition, Professor Chen Zhou ( School of Economics, Erasmus University Rotterdam and Senior Economist, De Nederlandsche Bank) and Dr Robert Yuen (Director of Advanced Analytics & Modeling, Liberty Mutual Insurance Group) will be advisors for this project and ensure that the programme of work includes questions of high priority to end users, which makes the project inherently impactful.

HOW TO APPLY

Applicants should submit an application for postgraduate study via the online application service for: http://www.cardiff.ac.uk/study/postgraduate/research/programmes/programme/mathematics

In the research proposal section of your application, please specify the project title and supervisors of this project.
If you are applying for more than one Cardiff University project please note this in the research proposal section.