Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-27T22:37:48.403Z Has data issue: false hasContentIssue false
  • English
  • Français

The Modelling of Extreme Events

Published online by Cambridge University Press:  10 June 2011

D. E. A. Sanders
D. E. A. Sanders
Affiliation:
Milliman Ltd, Finsbury Tower, 103-105 Bunhill Row, London EC1Y 8LZ, U.K. Tel: +44(0)20 7847 6186, Fax: +44(0)20 7847 6105; Email: david.sanders@milliman.com
Get access Rights & Permissions [Opens in a new window]

Abstract

The modelling of extreme events is becoming of increased importance to actuaries. This paper outlines the various theories. It outlines the consistent theory underlying many of the differing approaches and gives examples of the analysis of models. A review of non-standard extreme events is given, and issues of public policy are outlined.

Keywords

Extreme EventsExtreme Value TheoryGeneralised Pareto DistributionPower LawCat Models
Type
Sessional meetings: papers and abstracts of discussions
Information
British Actuarial Journal , Volume 11 , Issue 3 , 01 August 2005 , pp. 519 - 557
Copyright
Copyright © Institute and Faculty of Actuaries 2005

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Beard, R.E. (1962). Statistical theory of extreme values and an application to excess of loss reinsurance, (mimeographed MS, 1962)Google Scholar
Bak, P. (1996). How nature works: the science of self-organised criticality. Copernicus, New York.CrossRefGoogle Scholar
Bak, P., Tang, C. & Wiesenfeld, K. (1987). Self-organized criticality: an explanation of 1/f noise. Phys. Rev. Lett., 59, 381–384.CrossRefGoogle ScholarPubMed
Beelders, M. & Colarossi, D. (2004). Modelling mortality risk with extreme value theory. GARP, Issue 19.Google Scholar
Coles, S.G. (2001). An introduction to statistical modelling of extreme values. Springer Verlag, New York.CrossRefGoogle Scholar
Dessai, S. & Walter, M.E. (2003). Self-organised criticality and the atmospheric sciences: selected review, new findings and future directions.Google Scholar
Dunbar, N. (2001). Inventing money. Wiley.Google Scholar
Embrechts, P., Daniellson, J., Goodhart, C., Keating, C., Muenning, F., Renualt, O. & Shin, H.S. (2001). An academic response to Basel II. Financial Markets Group, London School of Economics.Google Scholar
Embrechts, P., Kluppelberg, C. & Mikosch, T. (1997). Modelling extremal events for insurance and finance. Springer, New York.CrossRefGoogle Scholar
Embrechts, P., Lindskog, F. & McNeil, A.J. (2003). Modelling dependence with copulas and applications to risk management. In Handbook of heavy tailed distributions in finance. Edited by Rachev, S.T.Elsevier/North-Holland, Amsterdam.Google Scholar
Embrechts, P., Mcneil, A.J. & Straumann, D. (1999). Correlation: pitfalls and alternatives. Risk, May 1999, 69–71.Google Scholar
Falk, M., Husler, J. & Reiss, R. (1994). Laws of small numbers: extremes and rare events. Birkhauser, Basel.Google Scholar
Finkenstadt, B. & Rootzen, H. (2003). Extreme values in finance, telecommunications, and the environment. Chapman and Hall.CrossRefGoogle Scholar
Fisher, R.A. & Tippett, L.H.C. (1928). Limiting forms of the frequency distributions of the largest or smallest member of a sample. Proceedings of the Cambridge Philosophical Society, 24, 180–190.CrossRefGoogle Scholar
Fougeres, A.-L. (2002). Multivariate extremes. In Finkenstadt & Rootzen, 373–388.Google Scholar
Gnedenko, B.V. (1943). Sur la distribution limite du terme maximum d'une serie aleatoire. Annals of Mathematics, 44, 423–453.CrossRefGoogle Scholar
Gumbel, E.J. (1958). Statistics of extremes. Columbia University Press.CrossRefGoogle Scholar
Gurenko, E.N. (ed.) (2004). Catastrophe risk and reinsurance. Risk Books.CrossRefGoogle Scholar
Hogg, R. & Klugman, S. (1984). Loss distributions. Wiley, New York.CrossRefGoogle Scholar
Kleiber, K. & Kotz, S. (2003). Statistical size distributions in economics and actuarial sciences. John Wiley, New Jersey.CrossRefGoogle Scholar
McNeil, A. (1997). Estimating the tails of loss severity distributions using extreme value theory, ASTIN Bulletin, 27, 117–137.CrossRefGoogle Scholar
Pickands, J. (1975). Statistical inference using extreme order statistics. Annals of Statistics, 3, 119–131.Google Scholar
Reiss, R. & Thomas, M. (1997). Statistical analysis of extreme values. Birkhauser (includes documentation for Xtremes software package).CrossRefGoogle Scholar
Resnick, S. (1987). Extreme values, point processes and regular variation. Springer Verlag, New York.CrossRefGoogle Scholar
Sanders, D.E.A. (1995). When the wind blows, an introduction to catastrophe excess of loss insurance. C.A.S. Fall Forum 1995.Google Scholar
Sanders, D.E.A. (2003). Extreme events part 2. Financial catastrophes. The overthrow of modern financial theory. GIRO 2003.Google Scholar
Sanders, D.E.A., Grealy, P., Hitchcox, A., Magnusson, T., Manjrekar, R., Ross, J., Shepley, S. & Waters, L. (1995). Pricing in the London Market. GIRO 1995.Google Scholar
Sanders, D.E.A., Brix, A., Duffy, P., Forster, W., Hartington, A., Jones, G., Levi, C., Paddam, P., Papachristou, D., Perry, G., Rix, S., Ross, F., Smith, A.J., Seth, A., Westcott, D. & Wilkinson, M. (2002). The management of losses arising from extreme events. GIRO 2002.Google Scholar
Smith, R.L. (1986). Extreme value theory based on the largest annual events. Journal of Hydrology, 86, 27–43.CrossRefGoogle Scholar
Smith, R.L. (2003). Statistics of extremes with applications in environment, insurance and finance. In Finkenstadt & Rootzen, 1–68.CrossRefGoogle Scholar
Smith, R.L. & Goodman, D. (2000). Bayesian risk analysis. Chapter 17 of Extremes and integrated risk management. Edited by Embrechts, P.. Risk Books, London.Google Scholar
Thom, R. (1989). Structural stability and morphogenesis. Addison Wesley Publishing Company.Google Scholar
Woo, G. (1999). The mathematics of natural catastrophes. Imperial College Press.CrossRefGoogle Scholar