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Risks 2014, 2(3), 289-314; doi:10.3390/risks2030289

Joint Asymptotic Distributions of Smallest and Largest Insurance Claims

1
Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, 1015 Lausanne, Switzerland
2
Swiss Finance Institute, Lausanne 1015, Switzerland
3
Université de Lyon, Université Lyon 1, Institut de Science Financière et d'Assurances,Lyon 69007, France
4
Department of Mathematics, University of Leuven, Leuven 3001, Belgium
*
Author to whom correspondence should be addressed.
Received: 25 February 2014 / Revised: 15 June 2014 / Accepted: 15 July 2014 / Published: 31 July 2014
(This article belongs to the Special Issue Risk Management Techniques for Catastrophic and Heavy-Tailed Risks)
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Abstract

Assume that claims in a portfolio of insurance contracts are described by independent and identically distributed random variables with regularly varying tails and occur according to a near mixed Poisson process. We provide a collection of results pertaining to the joint asymptotic Laplace transforms of the normalised sums of the smallest and largest claims, when the length of the considered time interval tends to infinity. The results crucially depend on the value of the tail index of the claim distribution, as well as on the number of largest claims under consideration. View Full-Text
Keywords: aggregate claims; ammeter problem; near mixed Poisson process; reinsurance; subexponential distributions; extremes aggregate claims; ammeter problem; near mixed Poisson process; reinsurance; subexponential distributions; extremes
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Albrecher, H.; Robert, C.Y.; Teugels, J.L. Joint Asymptotic Distributions of Smallest and Largest Insurance Claims. Risks 2014, 2, 289-314.

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