IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v65y2015icp94-102.html
   My bibliography  Save this article

Risk models with premiums adjusted to claims number

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668715001468
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2015.09.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    4. 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.
    5. Osatakul, Dhiti & Li, Shuanming & Wu, Xueyuan, 2023. "Discrete-time risk models with surplus-dependent premium corrections," Applied Mathematics and Computation, Elsevier, vol. 437(C).
    6. 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.
    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. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Cheung, Eric C.K. & Ni, Weihong & Oh, Rosy & Woo, Jae-Kyung, 2021. "Bayesian credibility under a bivariate prior on the frequency and the severity of claims," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 274-295.
    2. Lu, Yi & Li, Shuanming, 2005. "On the probability of ruin in a Markov-modulated risk model," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 522-532, December.
    3. Tzougas, George & Pignatelli di Cerchiara, Alice, 2021. "The multivariate mixed Negative Binomial regression model with an application to insurance a posteriori ratemaking," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 602-625.
    4. Tzougas, George & Yik, Woo Hee & Mustaqeem, Muhammad Waqar, 2019. "Insurance ratemaking using the Exponential-Lognormal regression model," LSE Research Online Documents on Economics 101729, London School of Economics and Political Science, LSE Library.
    5. Su, Jianxi & Furman, Edward, 2017. "Multiple risk factor dependence structures: Distributional properties," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 56-68.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:65:y:2015:i:c:p:94-102. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.