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2020 | OriginalPaper | Chapter

Chapter X: Dependence and Further Topics in Risk Management

Authors : Søren Asmussen, Mogens Steffensen

Published in: Risk and Insurance

Publisher: Springer International Publishing

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Abstract

In an abundance of settings, one will as a first modeling attempt assume independence of the r.v.s involved. This is mathematically very convenient but extremely dangerous: in many situations where a disastrous event occurred despite its risk being calculated to be so low that it could be neglected for any practical purpose, a back mirror analysis has revealed that the reason was precisely the simultaneous occurrence of events assumed to be independent when doing the risk calculation. The study of dependence and how it may be modeled is therefore crucial, and this is the topic of this chapter.

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previous chapter Chapter IX: Extreme Value Theory
next chapter Chapter XI: Stochastic Control in Non-Life Insurance
Footnotes
1
A risk measure ϱ may be defined on the class of all r.v.s X or a subclass such as those with \({\mathbb E} |X|<\infty \) or, more generally, L p with 1 ≤ p ≤∞.
 
2
For the moment, just think of the case of identical marginals where comonotonicity means X 1 = ⋯ = X n. For the general case, see Sect. 2.
 
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Metadata
Title
Chapter X: Dependence and Further Topics in Risk Management
Authors
Søren Asmussen
Mogens Steffensen
Copyright Year
2020
Book
Risk and Insurance

Print ISBN: 978-3-030-35175-5

Electronic ISBN: 978-3-030-35176-2

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-35176-2_10