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Swiss portfolio damaged in a hail storm over a specific time period. For details, see Schmock (1997). Further interesting new products are the multiline, multiyear, high-layer (infrequent event) products, credit lines, and the catastrophe risk exchange (CATEX). For a brief review of some of these instruments, see Punter (1997). Excellent overviews stressing the financial engineering of such products are Doherty (1997) and Tilley (1997). Alternative risk transfer and securitization have become major areas of applied research in both the banking and insurance industries. Actuaries are actively taking part in some of the new product development and therefore have to consider the methodological issues underlying these and similar products. Also, similar methods have recently been introduced into the world of finance through the estimation of value at risk (VaR) and the so-called shortfall; see Bassi, Embrechts, and Kafetzaki (1998) and Embrechts, Samorodnitsky, and Resnick (1998). ‘‘Value At Risk for End-Users’’ (1997) contains a recent summary of some of the more applied issues. More generally, extremes matter eminently within the world of finance. It is no coincidence that Alan Greenspan, chairman of the U.S. Federal Reserve, remarked at a research conference on risk measurement and systemic risk (Washington, D.C., November 1995) that ‘‘Work that characterizes the statistical distribution of extreme events would be useful, as well.’’ For the general observer, extremes in the realm of finance manifest themselves most clearly through stock market crashes or industry losses. In Figure 1, we have plotted the events leading up to and including the 1987 crash for equity data (S&P). Extreme value theory (EVT) yields methods for quantifying such events and their consequences in a statistically optimal way. (See McNeil 1998 for an interesting discussion of the 1987 crash example.) For a general equity book, for instance, a risk manager will be interested in estimating the resulting down-side risk, which typically can be reformulated in terms of a quantile for a profit-and-loss function. EVT is also playing an increasingly important role in credit risk management. The interested reader may browse J.P. Morgan’s web site (http://www. jpmorgan.com) for information on CreditMetrics. It is no coincidence that big investment banks are looking at actuarial methods for the sizing of reserves to guard against future credit losses. Swiss Bank Corporation, for instance, introduced actuarial credit risk accounting (ACRA) for credit risk management; see Figure 2. In their risk measurement framework, they use the following definitions: • Expected loss: the losses that must be assumed to arise on a continuing basis as a consequence of undertaking particular business • Unexpected loss: the unusual, though predictable, losses that the bank should be able to absorb in the normal course of its business • Stress loss: the possible—although improbable— extreme scenarios that the bank must be able to survive