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Stochastic comparisons for allocations of policy limits and deductibles with applications

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  • Lu, ZhiYi
  • Meng, LiLi

Abstract

In this paper, we study the problem of comparing losses of a policyholder who has an increasing utility function when the form of coverage is policy limit and deductible. The total retained losses of a policyholder are ordered in the usual stochastic order sense when Xi(i=1,...,n) are ordered with respect to the likelihood ratio order. The parallel results for the case of deductibles are obtained in the same way. It is shown that the ordering of the losses are related to the characteristics (log-concavity or log-convexity) of distributions of the risks. As an application of the comparison results, the optimal problems of allocations of policy limits and deductibles are studied in usual stochastic order sense and the closed-form optimal solutions are obtained in some special cases.

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  • Lu, ZhiYi & Meng, LiLi, 2011. "Stochastic comparisons for allocations of policy limits and deductibles with applications," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 338-343, May.
    • Handle: RePEc:eee:insuma:v:48:y:2011:i:3:p:338-343
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    References listed on IDEAS

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    6. Zhuang, Weiwei & Chen, Zijin & Hu, Taizhong, 2009. "Optimal allocation of policy limits and deductibles under distortion risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 409-414, June.
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    Cited by:

    1. Manesh, Sirous Fathi & Khaledi, Baha-Eldin & Dhaene, Jan, 2016. "Optimal allocation of policy deductibles for exchangeable risks," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 87-92.
    2. Manesh, Sirous Fathi & Khaledi, Baha-Eldin, 2015. "Allocations of policy limits and ordering relations for aggregate remaining claims," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 9-14.
    3. Cai, Jun & Wei, Wei, 2014. "Some new notions of dependence with applications in optimal allocation problems," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 200-209.
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    5. Yinping You & Xiaohu Li, 2017. "Most unfavorable deductibles and coverage limits for multiple random risks with Archimedean copulas," Annals of Operations Research, Springer, vol. 259(1), pages 485-501, December.
    6. Yinping You & Xiaohu Li & Rui Fang, 2021. "On coverage limits and deductibles for SAI loss severities," Annals of Operations Research, Springer, vol. 297(1), pages 341-357, February.
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    8. Li, Xiaohu & You, Yinping, 2012. "On allocation of upper limits and deductibles with dependent frequencies and comonotonic severities," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 423-429.
    9. Qi Feng & J. George Shanthikumar, 2018. "Arrangement Increasing Resource Allocation," Methodology and Computing in Applied Probability, Springer, vol. 20(3), pages 935-955, September.

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