How to Model Operational Risk, If You Must. Lecture to The Faculty of Actuaries

The second Lecturer to the Faculty of Actuaries is Professor Paul Embrechts, Professor of Mathematics at the ETH Zurich (Swiss Federal Institute of Technology, Zurich), specialising in actuarial mathematics and mathematical finance. His previous academic positions include ones at the Universities of Leuven, Limburg and London (Imperial College), and he has held visiting appointments at various other universities. He is an elected Fellow of the Institute of Mathematical Statistics, an Honorary Fellow of the Institute of Actuaries, a Corresponding Member of the Italian Institute of Actuaries, Editor of the ASTIN Bulletin, on the Advisory Board of Finance and Stochastics and Associate Editor of numerous scientific journals. He is a member of the Board of the Swiss Association of Actuaries and belongs to various national and international research and academic advisory committees. His areas of specialisation include insurance risk theory, integrated risk management, the interplay between insurance and finance and the modelling of rare event

Longevity risks and capital markets: The 2010-2011 update

This Special Issue of Geneva Papers on Risk and Insurance - Issues and Practice contains 10 contributions to the academic literature all dealing with longevity risk and capital markets. Draft versions of the papers were presented at Longevity Six: The Sixth International Longevity Risk and Capital Markets Solutions Conference that was held in Sydney on 9-10 September 2010. It was hosted by the Australian Institute for Population Ageing Research, the Australian School of Business and the University of New South Wales. It was sponsored by PricewaterhouseCoopers, Australian Prudential Regulation Authority (APRA), Coventry Capital, Swiss Re, and Institute of Actuaries of Australia.Longevity Risk; Capital Market

TIME DELAYS AND THE UNDERWRITING CYCLE

We shall consider the concept of time delays and the extent to which this is a common feature in many general insurance systems. We shall then present an example of a model of an insurance system with delays that helps to explain the phenomenon of underwriting cycles.insurance, time delays, underwriting cycle, forecasting, rating formula

Time Delays and The Underwriting Cycle

We shall consider the concept of time delays and the extent to which this is a common feature in many general insurance systems. We shall then present an example of a model of an insurance system with delays that helps to explain the phenomenon of underwriting cycles.insurance, time delays, underwriting cycle, forecasting, rating formula.

A Comparison of Nonparametric Methods in the Graduation of Mortality: Application to Data from the Valencia Region (Spain)

[EN] The nonparametric graduation of mortality data aims to estimate death rates by carrying out a smoothing of the crude rates obtained directly from original data. The main difference with regard to parametric models is that the assumption of an age-dependent function is unnecessary, which is advantageous when the information behind the model is unknown, as one cause of error is often the choice of an inappropriate model. This paper reviews the various alternatives and presents their application to mortality data from the Valencia Region, Spain. The comparison leads us to the conclusion that the best model is a smoothing by means of Generalised Additive Models (GAM) with splines. The most interesting part of this paper is the development of a plan that can be applied to mortality data for a wide range of age groups in any geographical area, allowing the most appropriate table to be chosen for the data in hand.The authors are indebted to the anonymous referees whose suggestions improved the original manuscript. This work was partially supported by a grant from MEyC (Ministerio de Educación y Ciencia, Spain, project MTM-2004-06231).The research of Francisco Montes has also been partially supported by a grant from DGITT (Direcció General d Investigació i Transferència Tecnològica de la Generalitat Valenciana, Project GRUPOS03/189).Debón Aucejo, AM.; Montes-Suay, F.; Sala-Garrido, R. (2006). A Comparison of Nonparametric Methods in the Graduation of Mortality: Application to Data from the Valencia Region (Spain). International Statistical Review. 74(2):215-233. https://doi.org/10.1111/j.1751-5823.2006.tb00171.xS215233742Bloomfield, D. S. F., & Haberman, S. (1987). Graduation: some experiments with kernel methods. Journal of the Institute of Actuaries, 114(2), 339-369. doi:10.1017/s0020268100019090Breiman, L., & Peters, S. (1992). Comparing Automatic Smoothers (A Public Service Enterprise). International Statistical Review / Revue Internationale de Statistique, 60(3), 271. doi:10.2307/1403679Brockmann, M., Gasser, T., & Herrmann, E. (1993). Locally Adaptive Bandwidth Choice for Kernel Regression Estimators. Journal of the American Statistical Association, 88(424), 1302-1309. doi:10.1080/01621459.1993.10476411Chan,, F. Y., Chan, L. K., Falkenberg, J., & Yu, M. H. (1986). Applications of linear and quadratic programmings to some cases of the Whittaker-Henderson graduation method. Scandinavian Actuarial Journal, 1986(3-4), 141-153. doi:10.1080/03461238.1986.10413805Clements, M. S. (2005). Lung cancer rate predictions using generalized additive models. Biostatistics, 6(4), 576-589. doi:10.1093/biostatistics/kxi028Cleveland, W. S. (1979). Robust Locally Weighted Regression and Smoothing Scatterplots. Journal of the American Statistical Association, 74(368), 829-836. doi:10.1080/01621459.1979.10481038Copas, J. B., & Haberman, S. (1983). Non-parametric graduation using kernel methods. Journal of the Institute of Actuaries, 110(01), 135-156. doi:10.1017/s0020268100041275Epanechnikov, V. A. (1969). Non-Parametric Estimation of a Multivariate Probability Density. Theory of Probability & Its Applications, 14(1), 153-158. doi:10.1137/1114019Felipe, A., Guillen, M., & Perez-Marin, A. M. (2002). Recent Mortality Trends in the Spanish Population. British Actuarial Journal, 8(4), 757-786. doi:10.1017/s1357321700003901Forfar, D. O., McCutcheon, J. J., & Wilkie, A. D. (1988). On graduation by mathematical formula. Journal of the Institute of Actuaries, 115(1), 1-149. doi:10.1017/s0020268100042633Gasser, T., Kneip, A., & Köhler, W. (1991). A Flexible and Fast Method for Automatic Smoothing. Journal of the American Statistical Association, 86(415), 643-652. doi:10.1080/01621459.1991.10475090Gasser, T., & Müller, H.-G. (1979). Kernel estimation of regression functions. Smoothing Techniques for Curve Estimation, 23-68. doi:10.1007/bfb0098489Gavin, J. B., Haberman, S., & Verrall, R. J. (1994). On the choice of bandwidth for kernel graduation. Journal of the Institute of Actuaries, 121(1), 119-134. doi:10.1017/s0020268100020102Guillen, M., Nielsen, J. P., & Perez-Marin, A. M. (2006). Multiplicative Hazard Models for Studying the Evolution of Mortality. Annals of Actuarial Science, 1(1), 165-177. doi:10.1017/s1748499500000099Heligman, L., & Pollard, J. H. (1980). The age pattern of mortality. Journal of the Institute of Actuaries, 107(1), 49-80. doi:10.1017/s0020268100040257Hoem, J. M., & Linnemann, P. (1988). The tails in moving average graduation. Scandinavian Actuarial Journal, 1988(4), 193-229. doi:10.1080/03461238.1988.10413848McCullagh, P., & Nelder, J. A. (1989). Generalized Linear Models. doi:10.1007/978-1-4899-3242-6Nadaraya, E. A. (1964). On Estimating Regression. Theory of Probability & Its Applications, 9(1), 141-142. doi:10.1137/1109020Nielsen, J. P. (2003). Smoothing and Prediction with a View to Actuarial Science, Biostatistics and Finance. Scandinavian Actuarial Journal, 2003(1), 51-74. doi:10.1080/03461230308484Silverman, B. W. (1984). A Fast and Efficient Cross-Validation Method for Smoothing Parameter Choice in Spline Regression. Journal of the American Statistical Association, 79(387), 584-589. doi:10.1080/01621459.1984.10478084Verrall, R. J. (1993). Graduation by dynamic regression methods. Journal of the Institute of Actuaries, 120(1), 153-170. doi:10.1017/s002026810003688xWang, J.-L., Müller, H.-G., & Capra, W. B. (1998). Analysis of oldest-old mortality: lifetables revisited. The Annals of Statistics, 26(1), 126-163. doi:10.1214/aos/1030563980Whittaker, E. T. (1922). On a New Method of Graduation. Proceedings of the Edinburgh Mathematical Society, 41, 63-75. doi:10.1017/s0013091500077853Zhang, H. (2004). Mixed effects multivariate adaptive splines model for the analysis of longitudinal and growth curve data. Statistical Methods in Medical Research, 13(1), 63-82. doi:10.1191/0962280204sm353r

International Adverse Selection in Life Insurance and Annuities

This paper evaluates the extent of adverse selection in life insurance and annuities in international markets, for both group and individual products. We also compare results with prior analyses of adverse selection in international annuity markets, focusing on the US, the UK, and Japan. Our results help assess the extent to which life insurers can hedge mortality exposure by writing both life insurance and annuities, and they may be used to determine a normal range for adverse selection in international insurance markets.

Multiperiod Statistical Risk Management Methods and Equity-Linked Life Insurance

We re-examine some statistical aspects of the task force report by Canadian Institute of Actuaries on the segregated fund investment guarantees. We argue that there can be non-trivial statistical problems involved for the equity-linked life insurances and investigate the statsitical properties of the multiperiod risk management methods including the moving quantile method and the block boortstrap method. Also we report some results of simulations and data analyses on the popular stock indices in Japan and Canada.

"Best-advice" and the "true" mortgate term. Actuaries' endowment advice principles revisited

In 1999 the Financial Services Authority recommended that a standard repayment mortgage was the “best advice” for Independent Financial Advisors to give to essentially all new mortgage customers seeking the best value repayment vehicle. The FSA simply followed the recommendation of the 1999 Report of the Endowment Mortgages Working Party of the Faculty and Institute of Actuaries. This working party compared the relative returns and risks with repayment and endowment mortgages over a standard twenty-five year term. Endowment mortgages benefit from compound rates of growth, and so the underlying capital value available for repayment increases disproportionately the longer returns are allowed to accumulate. In selecting between repayment and endowment mortgages, the true mortgage term of repayment therefore becomes the critical determinant of which repayment vehicle is actually the best value. Crucially, the FIA assumed that any variation in the length of mortgage would lead to a reduction in the standard twenty-five term, thus giving further weight to the preference for repayment mortgages as exhibiting better value. This study challenges the FIA’s Working Party assumption about the typical term of repayment in two ways. First, we draw on economists’ recent developments in consumer theory to show that the variation in needs-based expenditure among households is large enough to allow for a considerable cohort of the house-owning population to select to extend their mortgage term beyond twenty-five years. There is therefore no reason in theory why twenty-five years ought to be the upper limit for mortgage debt repayment. We then present the results of a study of a sample of mortgage applicants in the South East of England. These individual case study data are extremely rare, and so the results particularly valuable; and the principal result is that the “true” mortgage term for the largest single cohort of consumers is longer than 25 years. The results indicate that among those applicants trading up (around half of all mortgage applicants) the average extension associated with each move is two years. When this 27 year period is then taken as the standard repayment term, the results of any comparison of the effectiveness of repayment and endowment mortgages changes dramatically in favour of equity-backed investment plans. Simulations based on historic data demonstrate that endowment plans are 19.2% and ISA plans 21.6% more efficient than straight repayment mortgages over the longer period. Furthermore, the risk of an equity-backed investment plan under-performing is halved when the typical mortgage term is extended from twenty-five to twenty-seven years. We therefore conclude that while the FSA’s “best advice” is indeed applicable to many borrowers, for the majority the reality is that equity-backed methods of mortgage repayment represent a significant improvement compared with the currently favoured repayment mortgages.