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Schmidt, Thorsten
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[Journal:] Risks [ISSN:] 2227-9091 [Publisher:] MDPI [Place:] Basel [Volume:] 2 [Year:] 2014 [Issue:] 1 [Pages:] 3-24
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.
shot-noise processes
tail dependence
catastrophe derivatives
marked point process
minimum-distance estimation
self-exciting processes
CAT bonds
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