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ECOMOR and LCR reinsurance with gamma-like claims

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  • Hashorva, Enkelejd
  • Li, Jinzhu

Abstract

Assuming that the claim sizes of an insurance company have a common distribution with gamma-like tail, we study the asymptotic tail behaviour of the reinsured amounts under the ECOMOR and LCR reinsurance treaties, respectively. Our novel results include a precise asymptotic expansion for the tail probability of the reinsured amounts under the ECOMOR treaty and tight asymptotic bounds for the LCR case. As a by-product we derive a precise asymptotic expansion for the tail of the product of independent regularly varying random variables.

Suggested Citation

  • Hashorva, Enkelejd & Li, Jinzhu, 2013. "ECOMOR and LCR reinsurance with gamma-like claims," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 206-215.
    • Handle: RePEc:eee:insuma:v:53:y:2013:i:1:p:206-215
    DOI: 10.1016/j.insmatheco.2013.05.004
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    References listed on IDEAS

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    1. Hashorva, Enkelejd, 2007. "On the asymptotic distribution of certain bivariate reinsurance treaties," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 200-208, March.
    2. Jiang, Jun & Tang, Qihe, 2008. "Reinsurance under the LCR and ECOMOR treaties with emphasis on light-tailed claims," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 431-436, December.
    3. Enkelejd Hashorva & Anthony G. Pakes & Qihe Tang, 2010. "Asymptotics of Random Contractions," Papers 1008.0126, arXiv.org.
    4. Asimit, Alexandru V. & Jones, Bruce L., 2008. "Asymptotic Tail Probabilities for Large Claims Reinsurance of a Portfolio of Dependent Risks," ASTIN Bulletin, Cambridge University Press, vol. 38(1), pages 147-159, May.
    5. Hashorva, Enkelejd & Pakes, Anthony G. & Tang, Qihe, 2010. "Asymptotics of random contractions," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 405-414, December.
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    Cited by:

    1. Peng, Liang, 2014. "Joint tail of ECOMOR and LCR reinsurance treaties," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 116-120.
    2. Xing-Fang Huang & Ting Zhang & Yang Yang & Tao Jiang, 2017. "Ruin Probabilities in a Dependent Discrete-Time Risk Model With Gamma-Like Tailed Insurance Risks," Risks, MDPI, vol. 5(1), pages 1-14, March.
    3. Braun, Alexander & Ben Ammar, Semir & Eling, Martin, 2019. "Asset pricing and extreme event risk: Common factors in ILS fund returns," Journal of Banking & Finance, Elsevier, vol. 102(C), pages 59-78.
    4. 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.
    5. Asimit, Alexandru V. & Chen, Yiqing, 2015. "Asymptotic results for conditional measures of association of a random sum," Insurance: Mathematics and Economics, Elsevier, vol. 60(C), pages 11-18.
    6. Wang, Bingjie & Li, Jinzhu, 2024. "Asymptotic results on tail moment for light-tailed risks," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 43-55.

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