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Modelling Extremal Events: For Insurance and Finance
Contains graphs and diagrams, used to illustrate shapes of distributions. This book shows real data examples in various ways.
648 pages, Hardcover
First published June 1, 2004
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Displaying 1 - 2 of 2 reviews
July 7, 2025
Lemma- and proof-heavy. I am pretty good at math & statistics (or at least used to be), but the text left me scouring the internet for definitions and explanations. The first six chapters floated above my head like a balloon whose string I just couldn't reach. The last two chapters soared above me, leaving contrails.
That's the bad news. The good news is the authors, having laid the theoretical foundation, take the reader by the hand into practical problems, albeit with difficult and imprecise solutions.
The theme of the book is this: most students of statistics understand how sums of sample observations work thanks to the Law of Large Numbers and the Central Limit Theorem. This text examines how maxima of sample observations behave, couching them in terms of problems like: you have 157 years of flood data. How high do you build a dike to protect against a 1000-year flood? Hint: it's not going to be a normal approximation.
Chapters 1 & 2 are reviews of ruin theory, the Law(s) of Large Numbers, and the Central Limit Theorem - familiar ground for anyone whose taken actuarial exams.
In Chapter 3 we switch from sums to extremes, introducing the three core families of tail distributions (Fréchet, Weibull, and Gumbel) and categorizing the underlying families of distributions that map onto these tail distributions, including (especially) heavy-tailed distributions.
Chapter 4 looks at upper order statistics (the 2nd largest, 3rd largest, etc. observation), not just the maxima.
Chapter 5 lays some groundwork for Chapter 6 where the authors look at techniques for fitting observations to the tail distributions through preliminary data analysis (q-q plots, mean excess function, ratio of maximum/sum) and parameter estimation.
Chapter 7 extends classical time series analysis to heavy tailed distributions. Chapter 8 looks at special cases including a look back to ruin theory, 'hot hands', and reinsurance treaties.
I came to this text as a 'remedial' step back from de Haas's Extreme Value Theory: An Introduction, itself suggested by Taleb's Statistical Consequences of Fat Tails: Real World Preasymptotics, Epistemology, and Applications.
A big thanks to St. Louis University who let me haunt the library (the first I've ever been in named for a Pope) for an afternoon until I figured out how to get the book on loan. And that was through MOBIUS, Missouri's interlibrary service who snagged me a copy from Mizzou's Ellis Library for a couple months. A big thanks to MOBIUS and Mizzou as well.
That's the bad news. The good news is the authors, having laid the theoretical foundation, take the reader by the hand into practical problems, albeit with difficult and imprecise solutions.
The theme of the book is this: most students of statistics understand how sums of sample observations work thanks to the Law of Large Numbers and the Central Limit Theorem. This text examines how maxima of sample observations behave, couching them in terms of problems like: you have 157 years of flood data. How high do you build a dike to protect against a 1000-year flood? Hint: it's not going to be a normal approximation.
Chapters 1 & 2 are reviews of ruin theory, the Law(s) of Large Numbers, and the Central Limit Theorem - familiar ground for anyone whose taken actuarial exams.
In Chapter 3 we switch from sums to extremes, introducing the three core families of tail distributions (Fréchet, Weibull, and Gumbel) and categorizing the underlying families of distributions that map onto these tail distributions, including (especially) heavy-tailed distributions.
Chapter 4 looks at upper order statistics (the 2nd largest, 3rd largest, etc. observation), not just the maxima.
Chapter 5 lays some groundwork for Chapter 6 where the authors look at techniques for fitting observations to the tail distributions through preliminary data analysis (q-q plots, mean excess function, ratio of maximum/sum) and parameter estimation.
Chapter 7 extends classical time series analysis to heavy tailed distributions. Chapter 8 looks at special cases including a look back to ruin theory, 'hot hands', and reinsurance treaties.
I came to this text as a 'remedial' step back from de Haas's Extreme Value Theory: An Introduction, itself suggested by Taleb's Statistical Consequences of Fat Tails: Real World Preasymptotics, Epistemology, and Applications.
A big thanks to St. Louis University who let me haunt the library (the first I've ever been in named for a Pope) for an afternoon until I figured out how to get the book on loan. And that was through MOBIUS, Missouri's interlibrary service who snagged me a copy from Mizzou's Ellis Library for a couple months. A big thanks to MOBIUS and Mizzou as well.
August 19, 2020
One of the very best.
Displaying 1 - 2 of 2 reviews