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On Heterogeneity In The Individual Model With Both Dependent Claim Occurrences And Severities

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  • Zhang, Yiying
  • Li, Xiaohu
  • Cheung, Ka Chun

Abstract

It is a common belief for actuaries that the heterogeneity of claim severities in a given insurance portfolio tends to increase its dangerousness, which results in requiring more capital for covering claims. This paper aims to investigate the effects of orderings and heterogeneity among scale parameters on the aggregate claim amount when both claim occurrence probabilities and claim severities are dependent. Under the assumption that the claim occurrence probabilities are left tail weakly stochastic arrangement increasing, the actuaries' belief is examined from two directions, i.e., claim severities are comonotonic or right tail weakly stochastic arrangement increasing. Numerical examples are provided to validate these theoretical findings. An application in assets allocation is addressed as well.

Suggested Citation

  • Zhang, Yiying & Li, Xiaohu & Cheung, Ka Chun, 2018. "On Heterogeneity In The Individual Model With Both Dependent Claim Occurrences And Severities," ASTIN Bulletin, Cambridge University Press, vol. 48(2), pages 817-839, May.
    • Handle: RePEc:cup:astinb:v:48:y:2018:i:02:p:817-839_00
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    Cited by:

    1. Ariyafar, Saeed & Tata, Mahbanoo & Rezapour, Mohsen & Madadi, Mohsen, 2020. "Comparison of aggregation, minimum and maximum of two risky portfolios with dependent claims," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    2. 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.
    3. Li, Chen & Li, Xiaohu, 2019. "Preservation of WSAI under default transforms and its application in allocating assets with dependent realizable returns," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 84-91.
    4. 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.

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