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Burnecki, Krzysztof
Giuricich, Mario Nicoló
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[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 5 [Year:] 2017 [Issue:] 4 [Pages:] 1-19
MDPI, Basel
We consider the subject of approximating tail probabilities in the general compound renewal process framework, where severity data are assumed to follow a heavy-tailed law (in that only the first moment is assumed to exist). By using the weak convergence of compound renewal processes to a-stable Lévy motion, we derive such weak approximations. Their applicability is then highlighted in the context of an existing, classical, index-linked catastrophe bond pricing model, and in doing so, we specialize these approximations to the case of a compound time-inhomogeneous Poisson process. We emphasize a unique feature of our approximation, in that it only demands finiteness of the first moment of the aggregate loss processes. Finally, a numerical illustration is presented. The behavior of our approximations is compared to both Monte Carlo simulations and first-order single risk loss process approximations and compares favorably.
index-linked catastrophe bonds
compound renewal process
compound Poisson process
heavy-tailed claims
table Lévy motion
weak convergence
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