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Stable Weak Approximation at Work in Index-Linked Catastrophe Bond Pricing

Krzysztof Burnecki and Mario Nicoló Giuricich ()
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Mario Nicoló Giuricich: Department of Actuarial Science, Faculty of Commerce, University of Cape Town, Rondebosch 7701, Cape Town, South Africa

Risks, 2017, vol. 5, issue 4, 1-19

Abstract: 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 α -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.

Keywords: index-linked catastrophe bonds; compound renewal process; compound Poisson process; heavy-tailed claims; α-table Lévy motion; weak convergence (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 M2 M4 K2 (search for similar items in EconPapers)
Date: 2017
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