IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v12y2010i3d10.1007_s11009-008-9116-0.html
   My bibliography  Save this article

A Saddlepoint Approximation to the Distribution of Inhomogeneous Discounted Compound Poisson Processes

Author

Listed:
  • Riccardo Gatto

    (University of Bern)

Abstract

In this article we propose an accurate approximation to the distribution of the discounted total claim amount, where the individual claim amounts are independent and identically distributed and the number of claims over a specified period is governed by an inhomogeneous Poisson process. More precisely, we compute cumulant generating functions of such discounted total claim amounts under various intensity functions and individual claim amount distributions, and invert them by the saddlepoint approximation. We provide precise conditions under which the saddlepoint approximation holds. The resulting approximation is numerically accurate, computationally fast and hence more efficient than Monte Carlo simulation.

Suggested Citation

  • Riccardo Gatto, 2010. "A Saddlepoint Approximation to the Distribution of Inhomogeneous Discounted Compound Poisson Processes," Methodology and Computing in Applied Probability, Springer, vol. 12(3), pages 533-551, September.
    • Handle: RePEc:spr:metcap:v:12:y:2010:i:3:d:10.1007_s11009-008-9116-0
    DOI: 10.1007/s11009-008-9116-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-008-9116-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-008-9116-0?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.

    Citations

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


    Cited by:

    1. Gatto, Riccardo, 2015. "A logarithmic efficient estimator of the probability of ruin with recuperation for spectrally negative Lévy risk processes," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 177-184.
    2. Riccardo Gatto, 2019. "Saddlepoint Approximation for Data in Simplices: A Review with New Applications," Stats, MDPI, vol. 2(1), pages 1-27, February.
    3. Riccardo Gatto, 2012. "Saddlepoint Approximations to Tail Probabilities and Quantiles of Inhomogeneous Discounted Compound Poisson Processes with Periodic Intensity Functions," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 1053-1074, December.
    4. Riccardo Gatto & Benjamin Baumgartner, 2014. "Value at Ruin and Tail Value at Ruin of the Compound Poisson Process with Diffusion and Efficient Computational Methods," Methodology and Computing in Applied Probability, Springer, vol. 16(3), pages 561-582, September.

    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:spr:metcap:v:12:y:2010:i:3:d:10.1007_s11009-008-9116-0. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.