Dependence Models for Actuarial Data.

When we fit a model to data, we are usually interested in representing the data the best way possible, and therefore in finding a model that fits the entire data set well. However, when the focus is on capturing the behaviour of extreme events - such as floods or large financial losses, for example - these models won't perform well. As a solution, extreme value methods can be applied to model only the data in the tail. But what about the situation where the non-extreme data are also of interest? When the data available concerns a single variable - for example, the modelling of the rainfall distribution at a particular location - there are statistical methods available that aim to accurately model the body of the distribution (i.e., data that aren't extreme) and the tail of the distribution (i.e., extreme events). However, when we have more than one variable - for example when an actuary is interested in modelling the dependence between liabilities in order to understand the exposure to risk - the situation is more complex, and sparse work has been done concerning the case where both extremes and the body are of interest. This project aims to fill this gap by investigating and developing dependence models which allow the tails to be considered appropriately, as well as accurately modelling the body of the data.

In partnership with University College Dublin.

This proposal will benefit (i) the UK economy and society, (ii) our industrial partners, (iii) the wider community of non-academic employers of doctoral graduates in STOR, (iv) the scientific disciplines of statistics and operational research and associated academic communities, (v) UK doctoral students in STOR, and (vi) the CDT students themselves.

Below we outline how each of these communities will realise these benefits:

(i) The UK economy will gain a competitive edge through a significant increase in the supply and diversity of doctoral STOR professionals with the skills required to undertake influential, responsible and impactful research, and who have been trained to become future leaders. Our goal is that our future alumni who enter industry assume leading roles in realising the major impact that STOR can make in achieving effective data driven decision-making. Our existing alumni are already starting to achieve this. A wider societal benefit will accrue from research contributions to EPSRC Prosperity Outcomes, e.g. to the UK being a Productive and Resilient Nation.

(ii) Our industrial partners will particularly benefit from the skills supply identified in item (i), as likely employers of STOR-i graduates. They will further benefit from teaming with a community of leading edge STOR researchers in the solution of substantive industrial challenges. Mechanisms for the latter include doctoral projects co-supervised with industry, industrial internships, engagement in research clusters and industrial problem-solving days. Our training programme will give students the skills they need to ensure that research is conducted responsibly and that outcomes are successfully communicated to beneficiaries. The value that our industrial partners place on working with STOR-i can be seen through the pledged cash support of £1.7M.

(iii) A wider benefit will accrue from the employment of STOR-i graduates, equipped as described in items (i) and (ii), across non-partner public and private sector organisations. The breadth and depth of training provided by the CDT will enable students to quickly make a difference in these organisations, using their research skills to affect significant change.

(iv) The STOR academic community will benefit from methodological advances and from the increase and diversity in the supply of STOR researchers who value, and have experience of, collaborative research. Our alumni will be leaders in 21st Century Statistics with a strong culture of, and training in, reproducible research and a focus on achieving impact with excellence. Our recruitment strategy will further benefit this community in achieving a healthier supply of high-quality doctoral candidates from diverse backgrounds. Our research internship programme gives top mathematically able individuals from across the UK an experience of STOR research and has been shown to increase applications for STOR PhD programmes across the UK.

(v) Elements of the STOR-i programme will benefit the wider community of UK doctoral students in STOR. Using financial support from our industrial partners, we will continue our National Associate Scheme. This will provide up to 50 UK STOR doctoral students with funding and access to elements of STOR-i's training programme. An annual conference will provide opportunities for learning, networking and sharing research progress to members of the scheme.

(vi) STOR-i students will benefit from a personalised programme that will support each individual in fully achieving their research leadership potential, whether in academia or industry. Students will be given the tools and opportunities to develop research and broader skills that will enable them to achieve maximum scientific impact for their work. Our current alumni provide strong evidence that these future graduates will be extremely employable.