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Stochastic comparison of aggregate claim amounts between two heterogeneous portfolios and its applications

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  • Barmalzan, Ghobad
  • Najafabadi, Amir T. Payandeh
  • Balakrishnan, Narayanaswamy

Abstract

The aggregate claim amount in a particular time period is a quantity of fundamental importance for proper management of an insurance company and also for pricing of insurance coverages. In this paper, we show that the proportional hazard rates (PHR) model, which includes some well-known distributions such as exponential, Weibull and Pareto distributions, can be used as the aggregate claim amount distribution. We also present some conditions for the use of exponentiated Weibull distribution as the claim amount distribution. The results established here complete and extend the well-known result of Khaledi and Ahmadi (2008).

Suggested Citation

  • Barmalzan, Ghobad & Najafabadi, Amir T. Payandeh & Balakrishnan, Narayanaswamy, 2015. "Stochastic comparison of aggregate claim amounts between two heterogeneous portfolios and its applications," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 235-241.
    • Handle: RePEc:eee:insuma:v:61:y:2015:i:c:p:235-241
    DOI: 10.1016/j.insmatheco.2015.01.010
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    References listed on IDEAS

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    1. Saralees Nadarajah & Gauss Cordeiro & Edwin Ortega, 2013. "The exponentiated Weibull distribution: a survey," Statistical Papers, Springer, vol. 54(3), pages 839-877, August.
    2. Proschan, F. & Sethuraman, J., 1976. "Stochastic comparisons of order statistics from heterogeneous populations, with applications in reliability," Journal of Multivariate Analysis, Elsevier, vol. 6(4), pages 608-616, December.
    3. Frostig, Esther, 2001. "A comparison between homogeneous and heterogeneous portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 29(1), pages 59-71, August.
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    Cited by:

    1. Barmalzan, Ghobad & Akrami, Abbas & Balakrishnan, Narayanaswamy, 2020. "Stochastic comparisons of the smallest and largest claim amounts with location-scale claim severities," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 341-352.
    2. Zhang, Yiying & Zhao, Peng, 2015. "Comparisons on aggregate risks from two sets of heterogeneous portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 124-135.
    3. Hossein Nadeb & Hamzeh Torabi & Ali Dolati, 2018. "Stochastic comparisons of the largest claim amounts from two sets of interdependent heterogeneous portfolios," Papers 1812.08343, arXiv.org.
    4. Barmalzan, Ghobad & Payandeh Najafabadi, Amir T., 2015. "On the convex transform and right-spread orders of smallest claim amounts," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 380-384.
    5. Hossein Nadeb & Hamzeh Torabi & Ali Dolati, 2018. "Ordering the smallest claim amounts from two sets of interdependent heterogeneous portfolios," Papers 1812.06166, arXiv.org.
    6. Li, Chen & Li, Xiaohu, 2016. "Sufficient conditions for ordering aggregate heterogeneous random claim amounts," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 406-413.

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