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

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  • Dembińska, Anna
  • Buraczyńska, Aneta

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.

Suggested Citation

  • Dembińska, Anna & Buraczyńska, Aneta, 2019. "The long-term behavior of number of near-maximum insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 226-237.
    • Handle: RePEc:eee:insuma:v:88:y:2019:i:c:p:226-237
    DOI: 10.1016/j.insmatheco.2019.07.007
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    References listed on IDEAS

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    1. Eryilmaz, Serkan & Gebizlioglu, Omer L. & Tank, Fatih, 2011. "Modeling of claim exceedances over random thresholds for related insurance portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 496-500.
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    5. Li, Y. & Pakes, Anthony G., 2001. "On the number of near-maximum insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 28(3), pages 309-323, June.
    6. V. Chavez‐Demoulin & P. Embrechts, 2004. "Smooth Extremal Models in Finance and Insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 71(2), pages 183-199, June.
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