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Risks 2017, 5(4), 64; https://doi.org/10.3390/risks5040064

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

1
Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wroclaw University of Science and Technology, 50-370 Wroclaw, Poland
2
Department of Actuarial Science, Faculty of Commerce, University of Cape Town, Rondebosch 7701, Cape Town, South Africa
Current address: The African Institute for Financial Markets and Risk Management, University of Cape Town, South Africa.
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Received: 28 November 2017 / Revised: 12 December 2017 / Accepted: 13 December 2017 / Published: 16 December 2017
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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. View Full-Text
Keywords: index-linked catastrophe bonds; compound renewal process; compound Poisson process; heavy-tailed claims; α-table Lévy motion; weak convergence index-linked catastrophe bonds; compound renewal process; compound Poisson process; heavy-tailed claims; α-table Lévy motion; weak convergence
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. (CC BY 4.0).
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Burnecki, K.; Giuricich, M.N. Stable Weak Approximation at Work in Index-Linked Catastrophe Bond Pricing. Risks 2017, 5, 64.

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