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Allocations of policy limits and ordering relations for aggregate remaining claims

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  • Manesh, Sirous Fathi
  • Khaledi, Baha-Eldin

Abstract

Let X1,…,Xn be a set of n risks, with decreasing joint density function f, faced by a policyholder who is insured for this n risks, with upper limit coverage for each risk. Let l=(l1,…ln) and l∗=(l1∗,…ln∗) be two vectors of policy limits such that l∗ is majorized by l. It is shown that ∑i=1n(Xi−li)+ is larger than ∑i=1n(Xi−li∗)+ according to stochastic dominance if f is exchangeable. It is also shown that ∑i=1n(Xi−l(i))+ is larger than ∑i=1n(Xi−l(i)∗)+ according to stochastic dominance if either f is a decreasing arrangement or X1,…,Xn are independent and ordered according to the reversed hazard rate ordering. We apply the new results to multivariate Pareto distribution.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:65:y:2015:i:c:p:9-14
    DOI: 10.1016/j.insmatheco.2015.08.003
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    References listed on IDEAS

    as
    1. Cheung, Ka Chun, 2007. "Optimal allocation of policy limits and deductibles," Insurance: Mathematics and Economics, Elsevier, vol. 41(3), pages 382-391, November.
    2. 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.
    3. Hua, Lei & Cheung, Ka Chun, 2008. "Worst allocations of policy limits and deductibles," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 93-98, August.
    4. Xu, Maochao & Hu, Taizhong, 2012. "Stochastic comparisons of capital allocations with applications," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 293-298.
    5. 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.
    6. 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.
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    Cited by:

    1. Zhang, Yiying & Cheung, Ka Chun, 2020. "On the increasing convex order of generalized aggregation of dependent random variables," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 61-69.
    2. 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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