保險和金融用的例外事件模型

內(nèi)容概要

In a recent issue, The New Scientist ran a cover story under the title: "Mission improbable. How to predict the unpredictable"; see Matthews [448]. In it, the author describes a group of mathematicians who claim that extreme value theory (EVT) is capable of doing just that: predicting the occurrence of rare events, outside the range of available data. All members of this group, the three of us included, would immediately react with: "Yes, but, ...", or, "Be aware...". Rather than at this point trying to explain what EVT can and cannot do, we would like to quote two members of the group referred to in [448]. Richard Smith said, "There is always going to be an element of doubt, as one is extrapolating into areas one doesn't know about. But what EVT is doing is making the best use of whatever data you have about extreme phenomena." Quoting from Jonathan Tawn, "The key message .is that EVT cannot do magic - but it can do a whole lot better than empirical curvefitting and guesswork. My answer to the sceptics is that if people aren't given well-founded methods like EVT, they'll just use dubious ones instead."

書籍目錄

Reader Guidelines 1 Risk Theory   1.1 The Ruin Problem   1.2 The Cramer-Lundberg Estimate   1.3 Ruin Theory for Heavy-Tailed Distributions     1.3.1 Some Preliminary Results     1.3.2 Cramer-Lundberg Theory for Subexponential Distributions     1.3.3 The Total Claim Amount in the Subexponential Case   1.4 Cramer-Lundberg Theory for Large Claims: a Discussion     1.4.1 Some Related Classes of Heavy-Tailed Distributions     1.4.2 The Heavy-Tailed Cramer-Lundberg Case Revisited 2 Fluctuations of Sums   2.1 The Laws of Large Numbers   2.2 The Central Limit Problem   2.3 Refinements of the CLT   2.4 The Functional CLT: Brownian Motion Appears   2.5 Random Sums     2.5.1 General Randomly Indexed Sequences     2.5.2 Renewal Counting Processes     2.5.3 Random Sums Driven by Renewal Counting Processes 3 Fluctuations of Maxima  3.1  Limit Probabilities for Maxima  3.2  Weak Convergence of Maxima Under Affine Tranformations  3.3  Maximum Domains of Attracion and Norming Constants    3.3.1  The Mazimum Domain of Attraction of the Frechet Distribution     ……4  Fluctuations of Upper Order Statistics5  An Approach to Extremes via Point Processes6  Statistical Methods for Extremal Events7  Time Series Analysis for Heavy-Tailed Procces8  Special TopicsAppendixReferencesIndexList of Abbreviations and Symbols

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