Extreme Value Theory as a Risk Management Tool

Extreme Value Theory as a Risk Management Tool By Paul Embrechts, Sidney I. Resnick, and Gennady Samorodnitsky North American Actuarial Journal, Volume 3, Number 2, April 1999 Y Copyright 2010 by the Society of Actuaries, Schaumburg, Illinois. Posted with permission. Name /8042/03 04/21/99 09:19AM Plate # 0pg 30 # 130 NAAJ(SOA)EXTREMEVALUETHEORYAS ARISKMANAGEMENTTOOL*Paul Embrechts, Sidney I. Resnick, and Gennady Samorodnitsky ABSTRACTThe financial industry, including banking and insurance, is undergoing major changes. The(re)insurance industry is increasingly exposed to catastrophic losses for which the requested coveris only just available. An increasing complexity of financial instruments calls for sophisticated riskmanagement tools. The securitization of risk and alternative risk transfer highlight the conver-gence of finance and insurance at the product level. Extreme Value Theory plays an importantmethodological role within risk Management for insurance, reinsurance, and 1 California Earthquake Data1971 INTRODUCTIONC onsider the time series in Table 1 of loss ratios(yearly data) for earthquake insurance in Californiafrom 1971 through 1993.

Name /8042/03 04/21/99 09:19AM Plate # 0 pg 31 # 2 EXTREME VALUE THEORY AS A RISK MANAGEMENT TOOL 31 NAAJ (SOA) Figure 2 Actuarial Credit Risk Accounting (ACRA) Figure 1 1987 Crash Swiss portfolio damaged in a hail storm over a spe-

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