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Risks 2014, 2(1), 3-24; doi:10.3390/risks2010003
Article

Catastrophe Insurance Modeled by Shot-Noise Processes

Chemnitz University of Technology, Reichenhainer Str. 41, Chemnitz 09126, Germany
Received: 6 November 2013 / Revised: 28 January 2014 / Accepted: 29 January 2014 / Published: 21 February 2014
(This article belongs to the Special Issue Application of Stochastic Processes in Insurance)
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Abstract

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.
Keywords: shot-noise processes; tail dependence; catastrophe derivatives; marked point process; minimum-distance estimation; self-exciting processes; CAT bonds shot-noise processes; tail dependence; catastrophe derivatives; marked point process; minimum-distance estimation; self-exciting processes; CAT bonds
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Schmidt, T. Catastrophe Insurance Modeled by Shot-Noise Processes. Risks 2014, 2, 3-24.

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