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Joint Asymptotic Distributions of Smallest and Largest Insurance Claims

Hansjörg Albrecher (), Christian Y. Robert () and Jef L. Teugels ()
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Hansjörg Albrecher: Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, 1015 Lausanne, Switzerland
Christian Y. Robert: Université de Lyon, Université Lyon 1, Institut de Science Financière et d'Assurances,Lyon 69007, France
Jef L. Teugels: Department of Mathematics, University of Leuven, Leuven 3001, Belgium

Risks, 2014, vol. 2, issue 3, 1-26

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.

Keywords: aggregate claims; ammeter problem; near mixed Poisson process; reinsurance; subexponential distributions; extremes (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 M2 M4 K2 (search for similar items in EconPapers)
Date: 2014
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