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Risk models with premiums adjusted to claims number

Author

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  • Li, Bo
  • Ni, Weihong
  • Constantinescu, Corina

Abstract

Classical compound Poisson risk models consider the premium rate to be constant. By adjusting the premium rate to the claims history, one can emulate a Bonus–Malus system within the ruin theory context. One way to implement such adjustment is by considering the Poisson parameter to be a continuous random variable and use credibility theory arguments to adjust the premium rate a posteriori. Depending on the defectiveness of this random variable, respectively referred to as ‘unforeseeable’ (defective) versus ‘historical’ (non-defective) risks, one obtains different relations between the ruin probability with constant versus adjusted premium rate. A combination of these two kinds of risks also leads to a relation between the two ruin probabilities, when the a posteriori estimator of the number of claims is carefully chosen. Examples for specific claim sizes are presented throughout the paper.

Suggested Citation

  • Li, Bo & Ni, Weihong & Constantinescu, Corina, 2015. "Risk models with premiums adjusted to claims number," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 94-102.
    • Handle: RePEc:eee:insuma:v:65:y:2015:i:c:p:94-102
    DOI: 10.1016/j.insmatheco.2015.09.001
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    References listed on IDEAS

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    1. Ni, Weihong & Constantinescu, Corina & Pantelous, Athanasios A., 2014. "Bonus–Malus systems with Weibull distributed claim severities," Annals of Actuarial Science, Cambridge University Press, vol. 8(2), pages 217-233, September.
    2. Jasiulewicz, Helena, 2001. "Probability of ruin with variable premium rate in a Markovian environment," Insurance: Mathematics and Economics, Elsevier, vol. 29(2), pages 291-296, October.
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    Cited by:

    1. Dhiti Osatakul & Xueyuan Wu, 2021. "Discrete-Time Risk Models with Claim Correlated Premiums in a Markovian Environment," Risks, MDPI, vol. 9(1), pages 1-23, January.
    2. Jon Danielsson & Kevin R. James & Marcela Valenzuela & Ilknur Zer, 2016. "Can We Prove a Bank Guilty of Creating Systemic Risk? A Minority Report," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 48(4), pages 795-812, June.
    3. Wang, Zijia & Landriault, David & Li, Shu, 2021. "An insurance risk process with a generalized income process: A solvency analysis," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 133-146.
    4. Osatakul, Dhiti & Li, Shuanming & Wu, Xueyuan, 2023. "Discrete-time risk models with surplus-dependent premium corrections," Applied Mathematics and Computation, Elsevier, vol. 437(C).
    5. Ka-Meng Siu & Ka-Hou Chan & Sio-Kei Im, 2023. "A Study of Assessment of Casinos’ Risk of Ruin in Casino Games with Poisson Distribution," Mathematics, MDPI, vol. 11(7), pages 1-15, April.
    6. Corina Constantinescu & Suhang Dai & Weihong Ni & Zbigniew Palmowski, 2016. "Ruin Probabilities with Dependence on the Number of Claims within a Fixed Time Window," Risks, MDPI, vol. 4(2), pages 1-23, June.
    7. Liu, Yang & Zhang, Xingfang & Ma, Weimin, 2017. "A new uncertain insurance model with variational lower limit," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 164-169.
    8. Wenhui Zhang & Yongmin Su & Ruimin Ke & Xinqiang Chen, 2018. "Evaluating the influential priority of the factors on insurance loss of public transit," PLOS ONE, Public Library of Science, vol. 13(1), pages 1-11, January.

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