Probability in Actuarial Science
This half-day meeting will bring together researchers and practitioners across actuarial science and applied probability to discuss topics of current research in actuarial mathematics. A particular focus will be on areas of interest to, and which can benefit from the expertise of, the applied probability community, with the aim of highlighting areas of common interest and developing links between experts working in these areas.
1pm Catherine Donnelly (Heriot-Watt University)
1.50pm Dan Georgescu (Bank of England)
3.10pm Ronnie Loeffen (University of Manchester)
4pm Andreas Tsanakas (Cass Business School)
Titles and abstracts:
Catherine Donnelly (Heriot-Watt University) - Capitalising on pensions freedom: reinventing the life annuity
Pensions freedom has meant that people no longer have to buy a life annuity contract with their retirement savings. However, there are advantages to life annuities that may not be apparent to the average consumer. We propose a way of making the main advantage - the increase in income due to mortality pooling - transparent, through a new way of pooling mortality together.
We also discuss the difficulties facing individuals in planning for their retirement, and consider how we could help through the development of new pension products.
This talk is based on joint work with Montserrat Guillen, Jens Perch Nielsen and John Young.
Dan Georgescu (Bank of England) - Explicit solutions to correlation matrix completion problems, with an application to insurance
I show how to derive explicit solutions to the problem of completing a partially specified correlation matrix. The results apply to several block structures for the unspecified entries that arise in insurance and risk management, where an insurance company with many lines of business is required to satisfy certain capital requirements but may have incomplete knowledge of the underlying correlation matrix. Among the many possible completions I focus on the one with maximal determinant because this has attractive properties. The explicit formulas enable easy solution of practical problems and are useful for testing algorithms for the general correlation matrix completion problem.
Preprint available at: http://eprints.ma.man.ac.uk/2585/
Ronnie Loeffen (University of Manchester) - On some optimal control problems in insurance
We go over a few stochastic optimal control problems that all involve controlling the economic capital of an insurance company. In particular we look at how to pay out dividends, how to inject capital and how much new business to take on. The focus is on examining when a particularly simple strategy is optimal in each case. We further discuss how these problems fit into the practical area of enterprise risk management.
Andreas Tsanakas (Cass Business School) - Reverse sensitivity testing
Sensitivity and uncertainty analyses are important components of model building, interpretation and validation. We propose a model-independent framework for sensitivity analysis that reflects sensitivity in the whole input and output distribution. A model comprises a vector of random input factors and an aggregation function, mapping risk factors to a random output. A typical example is that of an internal model used by an insurer to calculate capital requirements. Our reverse sensitivity testing method proceeds as follows. First, a stress on the model output distribution is specified, for example an increase in output VaR and/or Expected Shortfall. Second, a stressed model is identified, as a new probability measure that minimises the Kullback-Leibler divergence with respect to the baseline model, subject to constraints (stresses) on the output. Third, changes of the distribution of the inputs under the stressed model are assessed, thus identifying the key drivers of the stressed output. Implementation in a Monte-Carlo simulation setting is akin to importance sampling and thus numerically efficient, circumventing the need for the computationally expensive repeated evaluations of the aggregation function that are common in standard sensitivity analyses. We illustrate our approach through a numerical example of a simple insurance portfolio.
Authors: Silvana Pesenti, Pietro Millossovich, Andreas Tsanakas (all at Cass Business School, City, University of London)
Registration is required. The meeting is free to RSS Fellows; otherwise the cost is £20.
Organiser Name Fraser Daly and Neil Walton
Organising Group(s) RSS Applied Probability Section