Stable Weak Approximation at Work in Index-Linked Catastrophe Bond Pricing
Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wroclaw University of Science and Technology, 50-370 Wroclaw, Poland
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
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
-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.
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Burnecki, K.; Giuricich, M.N. Stable Weak Approximation at Work in Index-Linked Catastrophe Bond Pricing. Risks 2017, 5, 64.
Burnecki K, Giuricich MN. Stable Weak Approximation at Work in Index-Linked Catastrophe Bond Pricing. Risks. 2017; 5(4):64.
Burnecki, Krzysztof; Giuricich, Mario N. 2017. "Stable Weak Approximation at Work in Index-Linked Catastrophe Bond Pricing." Risks 5, no. 4: 64.
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