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Acts of God and ManRuminations on Risk and Insurance$
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Michael Powers

Print publication date: 2014

Print ISBN-13: 9780231153676

Published to Columbia Scholarship Online: November 2015

DOI: 10.7312/columbia/9780231153676.001.0001

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The Shapes of Things to Come

The Shapes of Things to Come

Probabilities and Parameters

Chapter:
(p.37) 3 The Shapes of Things to Come
Source:
Acts of God and Man
Author(s):

Michael R. Powers

Publisher:
Columbia University Press
DOI:10.7312/columbia/9780231153676.003.0003

This chapter examines complex probability distributions whose shapes make them appropriate for characterizing insurance and other financial risks. In particular, it introduces two important families of distributions: the Pareto family and the symmetric Lévy-stable family, both of which are frequently used to model particularly “risky” random variables with heavy tails (i.e. with large amounts of weight spread over the more extreme values of the random variable). To describe the measurement of risk, the chapter begins by defining the statistical moments of a distribution. It then shows how these quantities are used to compute the expected value (mean), standard deviation, and other helpful parameters.

Keywords:   probability distributions, financial risk, insurance risk, Pareto family, symmetric Lévy-stable family, random variables, risk measurement

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