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Reinsurance under the LCR and ECOMOR treaties with emphasis on light-tailed claims

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  • Jiang, Jun
  • Tang, Qihe

Abstract

Suppose that, over a fixed time interval of interest, an insurance portfolio generates a random number of independent and identically distributed claims. Under the LCR treaty the reinsurance covers the first l largest claims, while under the ECOMOR treaty it covers the first l-1 largest claims in excess of the lth largest one. Assuming that the claim sizes follow an exponential distribution or a distribution with a convolution-equivalent tail, we derive some precise asymptotic estimates for the tail probabilities of the reinsured amounts under both treaties.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:43:y:2008:i:3:p:431-436
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    References listed on IDEAS

    as
    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. Kremer, Erhard, 1985. "Finite formulae for the premium of the general reinsurance treaty based on ordered claims," Insurance: Mathematics and Economics, Elsevier, vol. 4(4), pages 233-238, October.
    3. 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.
    4. Kremer, Erhard, 1998. "Largest Claims Reinsurance Premiums under Possible Claims Dependence," ASTIN Bulletin, Cambridge University Press, vol. 28(2), pages 257-267, November.
    5. Embrechts, P. & Veraverbeke, N., 1982. "Estimates for the probability of ruin with special emphasis on the possibility of large claims," Insurance: Mathematics and Economics, Elsevier, vol. 1(1), pages 55-72, January.
    6. Kluppelberg, Claudia, 1989. "Estimation of ruin probabilities by means of hazard rates," Insurance: Mathematics and Economics, Elsevier, vol. 8(4), pages 279-285, 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. Claudia Kluppelberg & Miriam Isabel Seifert, 2016. "Conditional loss probabilities for systems of economic agents sharing light-tailed claims with analysis of portfolio diversification benefits," Papers 1612.07132, arXiv.org.
    3. 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.
    4. 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.
    5. Hashorva, Enkelejd & Li, Jinzhu, 2013. "ECOMOR and LCR reinsurance with gamma-like claims," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 206-215.
    6. Claudia Klüppelberg & Miriam Isabel Seifert, 2019. "Financial risk measures for a network of individual agents holding portfolios of light-tailed objects," Finance and Stochastics, Springer, vol. 23(4), pages 795-826, October.
    7. 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.

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