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Modeling of claim exceedances over random thresholds for related insurance portfolios

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  • Eryilmaz, Serkan
  • Gebizlioglu, Omer L.
  • Tank, Fatih

Abstract

Large claims in an actuarial risk process are of special importance for the actuarial decision making about several issues like pricing of risks, determination of retention treaties and capital requirements for solvency. This paper presents a model about claim occurrences in an insurance portfolio that exceed the largest claim of another portfolio providing the same sort of insurance coverages. Two cases are taken into consideration: independent and identically distributed claims and exchangeable dependent claims in each of the portfolios. Copulas are used to model the dependence situations. Several theorems and examples are presented for the distributional properties and expected values of the critical quantities under concern.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:insuma:v:49:y:2011:i:3:p:496-500
    DOI: 10.1016/j.insmatheco.2011.08.009
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    References listed on IDEAS

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    1. Jacek WesoĊ‚owski & Mohammad Ahsanullah, 1998. "Distributional Properties of Exceedance Statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(3), pages 543-565, September.
    2. Boutsikas, M. V. & Koutras, M. V., 2002. "Modeling claim exceedances over thresholds," Insurance: Mathematics and Economics, Elsevier, vol. 30(1), pages 67-83, February.
    3. Hashorva, Enkelejd, 2003. "On the number of near-maximum insurance claim under dependence," Insurance: Mathematics and Economics, Elsevier, vol. 32(1), pages 37-49, February.
    4. Ismihan Bairamov & Samuel Kotz, 2001. "On distributions of exceedances associated with order statistics and record values for arbitrary distributions," Statistical Papers, Springer, vol. 42(2), pages 171-185, April.
    5. Bairamov, Ismihan & EryIlmaz, Serkan, 2009. "Waiting times of exceedances in random threshold models," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 676-683, March.
    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.
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    Cited by:

    1. Erem, Aysegul & Bayramoglu, Ismihan, 2017. "Exact and asymptotic distributions of exceedance statistics for bivariate random sequences," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 181-188.

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