Catastrophe insurance modeled by shot-noise processes

Shot-noise processes generalize compound Poisson processes in the following way: a jump (the shot) is followed by a decline (noise). This constitutes a useful model for insurance claims in many circumstances; claims due to natural disasters or self-exciting processes exhibit similar features. We giv...

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Bibliographic Details
Published inRisks (Basel) Vol. 2; no. 1; pp. 3 - 24
Main Author Schmidt, Thorsten
Format Journal Article
LanguageEnglish
Published Basel MDPI 01.03.2014
MDPI AG
Subjects
CAT bonds
catastrophe derivatives
Catastrophes
Derivatives
Insurance industry
marked point process
minimum-distance estimation
Poisson distribution
self-exciting processes
shot-noise processes
Studies
tail dependence
Germany
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Summary:Shot-noise processes generalize compound Poisson processes in the following way: a jump (the shot) is followed by a decline (noise). This constitutes a useful model for insurance claims in many circumstances; claims due to natural disasters or self-exciting processes exhibit similar features. We give a general account of shot-noise processes with time-inhomogeneous drivers inspired by recent results in credit risk. Moreover, we derive a number of useful results for modeling and pricing with shot-noise processes. Besides this, we obtain some highly tractable examples and constitute a useful modeling tool for dynamic claims processes. The results can in particular be used for pricing Catastrophe Bonds (CAT bonds), a traded risk-linked security. Additionally, current results regarding the estimation of shot-noise processes are reviewed.
ISSN:2227-9091
2227-9091
DOI:10.3390/risks2010003