Extreme value statistics

In extreme value statistics similar regularities have emerged in the most surprising of areas - the extreme values we might have historically treated as awkward outliers. Can it be coincidence that complexity theory predicts inverse power law behaviour, extreme value theory predicts an inverse power pdf, and that empirically we find physical extremes of tides, rainfall, wind, and large losses in insurance showing pareto (inverse power pdf) distribution behaviour?

8.11 Conclusion: against the gods?

Global catastrophic risks are extensive, severe, and unprecedented. Insurance and business generally are not geared up to handling risks of this scale or type. Insurance can handle natural catastrophes such as earthquakes and windstorms, financial catastrophes such as stock market failures to some extent, and political catastrophes to a marginal extent. Insurance is best when there is an evidential basis and precedent for legal coverage. Business is best when the capital available matches the capital at risk and the return reflects the risk of loss of this capital. Global catastrophic risks unfortunately fail to meet any of these criteria. Nonetheless, the loss modelling techniques developed for the insurance industry coupled with our deeper understanding of uncertainty and new techniques give good reason to suppose we can deal with these risks as we have with others in the past. Do we believe the fatalist cliche that 'risk is the currency of the gods' or can we go 'against the gods' by thinking the causes and consequences of these emerging risks through, and then estimating their chances, magnitudes, and uncertainties? The history of insurance indicates that we should have a go! Acknowledgement

I thank Ian Nicol for his careful reading of the text and identification and correction of many errors. :

Suggestions for further reading

Banks, E. (2006). Catastrophic Risk (New York: John Wiley). Wiley Finance Series. This is a thorough and up-to-date text on the insurance and re-insurance of catastrophic risk. It explains clearly and simply the way computer models generate exceedance probability curves to estimate the chance of loss for such risks.

Buchanan, M. (2001). Ubiquity (London: Phoenix). This is a popular account - one of several now available including the same author's Small Worlds - of the 'inverse power' regularities somewhat surprisingly found to exist widely in complex systems. This is of particular interest to insurers as the long-tail probability distribution most often found for catastrophe risks is the pareto distribution which is 'inverse power'.

GIRO (2006). Report of the Catastrophe Modelling Working Party (London: Institute of Actuaries). This specialist publication provides a critical survey of the modelling methodology and commercially available models used in the insurance industry. References

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Malamud, B.D., Morein, G., and Turcotte, D.L. (1998). Forest fires - an example of self-organised critical behaviour. Science, 281, 1840-1842.

Sornette, D. (2004). Critical Phenomena in Natural Sciences - Chaos, Fractals,Selforganization and Disorder: Concepts and Tools, 2nd edition (Berlin: Springer).

Sornette, D., Malevergne, Y., and Muzy, J.F. (2003). Volatility fingerprints of large shocks: endogeneous versus exogeneous. Risk Magazine. Swiss Re. (2006). Swiss Re corporate survey 2006 report. Zurich: Swiss Re.

Swiss Re. (2007). Natural catastrophes and man-made disasters 2006. Sigma report no 2/2007. Zurich: Swiss Re.

Woo, G. (1999). The Mathematics of Natural Catastrophes (London: Imperial College


World Economic Forum. Global Risks 2006 (Geneva: World Economic Forum). World Economic Forum. Global Risks 2007 (Geneva: World Economic Forum). Yellman, T.W. (2000). The three facets of risk (Boeing Commercial Airplane Group, Seattle, WA) AIAA-2000-5594 2000. In World Aviation Conference, San Diego, CA, 10-12 October, 2000.

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