The long-term behavior of number of near-maximum insurance claims

Anna Dembińska and Aneta Buraczyńska

Insurance: Mathematics and Economics, 2019, vol. 88, issue C, 226-237

Abstract: A near-maximum insurance claim is one falling within a distance a of the current maximal claim. In this paper, we investigate asymptotic behavior of normalized numbers of near-maximum insurance claims under the assumption that the sequence of successive claim sizes forms a strictly stationary process. We present the results in a general form expressing limiting properties of normalized numbers of insurance claims that are in a left neighborhood of the mnth largest claim, where mn∕n tends to zero and n is the number of registered claims. We also give corollaries for sums of near-maximum insurance claims.

Keywords: Near-maximum insurance claim; Extreme and intermediate order statistics; Stationary process; Almost sure convergence; Limit theorems (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:88:y:2019:i:c:p:226-237

DOI: 10.1016/j.insmatheco.2019.07.007

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