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Ordering optimal deductible allocations for stochastic arrangement increasing risks

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  • Li, Chen
  • Li, Xiaohu

Abstract

The insurer usually solicits the insured through granting a certain amount of deductible to multiple risks according to his/her own will. Due to the nonlinear nature of the concerned optimization problem, in the literature on the optimal allocations of deductibles researchers usually assume independence or comonotonicity among concerned risks and ignore the impact due to frequency. In this study we build two sufficient conditions for the decreasing optimal allocation of deductibles, relaxing the stochastic arrangement increasing or right tail weakly stochastic arrangement increasing discount factors in Cai and Wei (2014, Theorems 6.3 and 6.6) to the conditionally upper orthant arrangement increasing or weak conditionally upper orthant arrangement increasing frequencies.

Suggested Citation

  • Li, Chen & Li, Xiaohu, 2017. "Ordering optimal deductible allocations for stochastic arrangement increasing risks," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 31-40.
    • Handle: RePEc:eee:insuma:v:73:y:2017:i:c:p:31-40
    DOI: 10.1016/j.insmatheco.2017.01.002
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    References listed on IDEAS

    as
    1. Hua, Lei & Cheung, Ka Chun, 2008. "Stochastic orders of scalar products with applications," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 865-872, June.
    2. Li, Xiaohu & Li, Chen, 2016. "On allocations to portfolios of assets with statistically dependent potential risk returns," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 178-186.
    3. 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.
    4. Cai, Jun & Wei, Wei, 2015. "Notions of multivariate dependence and their applications in optimal portfolio selections with dependent risks," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 156-169.
    5. 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.
    6. 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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    Cited by:

    1. Li, Chen & Li, Xiaohu, 2020. "Preservation of weak SAI’s under increasing transformations with applications," Statistics & Probability Letters, Elsevier, vol. 164(C).
    2. 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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