Joint asymptotic distributions of smallest and largest insurance claims

Hansjörg Albrecher, Christian Y. Robert and Jef L. Teugels
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Christian Y. Robert: LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon

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Abstract: 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 normalized 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)
Date: 2014-07-31
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Citations: View citations in EconPapers (2)

Published in Risks, 2014, ⟨10.3390/risks2030289⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01294387

DOI: 10.3390/risks2030289

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