Catastrophe Insurance Modeled by Shot-Noise Processes

Thorsten Schmidt
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Thorsten Schmidt: Chemnitz University of Technology, Reichenhainer Str. 41, Chemnitz 09126, Germany

Risks, 2014, vol. 2, issue 1, 1-22

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 (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (15)

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