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

Catastrophe Insurance Modeled by Shot-Noise Processes

Received: 6 November 2013; in revised form: 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 which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Schmidt, T. Catastrophe Insurance Modeled by Shot-Noise Processes. Risks 2014, 2, 3-24.

AMA Style

Schmidt T. Catastrophe Insurance Modeled by Shot-Noise Processes. Risks. 2014; 2(1):3-24.

Chicago/Turabian Style

Schmidt, Thorsten. 2014. "Catastrophe Insurance Modeled by Shot-Noise Processes." Risks 2, no. 1: 3-24.

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