IDEAS home Printed from https://ideas.repec.org/a/cup/astinb/v45y2015i03p601-637_00.html
   My bibliography  Save this article

Comparison Of Approximations For Compound Poisson Processes

Author

Listed:
  • Seri, Raffaello
  • Choirat, Christine

Abstract

In this paper, we compare the error in several approximation methods for the cumulative aggregate claim distribution customarily used in the collective model of insurance theory. In this model, it is usually supposed that a portfolio is at risk for a time period of length t. The occurrences of the claims are governed by a Poisson process of intensity μ so that the number of claims in [0,t] is a Poisson random variable with parameter λ = μ t. Each single claim is an independent replication of the random variable X, representing the claim severity. The aggregate claim or total claim amount process in [0,t] is represented by the random sum of N independent replications of X, whose cumulative distribution function (cdf) is the object of study. Due to its computational complexity, several approximation methods for this cdf have been proposed. In this paper, we consider 15 approximations put forward in the literature that only use information on the lower order moments of the involved distributions. For each approximation, we consider the difference between the true distribution and the approximating one and we propose to use expansions of this difference related to Edgeworth series to measure their accuracy as λ = μ t diverges to infinity. Using these expansions, several statements concerning the quality of approximations for the distribution of the aggregate claim process can find theoretical support. Other statements can be disproved on the same grounds. Finally, we investigate numerically the accuracy of the proposed formulas.

Suggested Citation

  • Seri, Raffaello & Choirat, Christine, 2015. "Comparison Of Approximations For Compound Poisson Processes," ASTIN Bulletin, Cambridge University Press, vol. 45(3), pages 601-637, September.
  • Handle: RePEc:cup:astinb:v:45:y:2015:i:03:p:601-637_00
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S0515036115000070/type/journal_article
    File Function: link to article abstract page
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. Marek Skarupski & Qinhao Wu, 2024. "Confidence bounds for compound Poisson process," Statistical Papers, Springer, vol. 65(8), pages 5351-5377, October.
    2. Matyas Barczy & Adam Dudas & Jozsef Gall, 2018. "On approximations of Value at Risk and Expected Shortfall involving kurtosis," Papers 1811.06361, arXiv.org, revised Dec 2020.
    3. Krzysztof Burnecki & Mario Nicoló Giuricich, 2017. "Stable Weak Approximation at Work in Index-Linked Catastrophe Bond Pricing," Risks, MDPI, vol. 5(4), pages 1-19, December.

    More about this item

    Statistics

    Access and download statistics

    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:cup:astinb:v:45:y:2015:i:03:p:601-637_00. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Kirk Stebbing (email available below). General contact details of provider: https://www.cambridge.org/asb .

    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.