IDEAS home Printed from https://ideas.repec.org/a/taf/lstaxx/v50y2021i24p5899-5917.html
   My bibliography  Save this article

The Erlang(n) risk model with two-sided jumps and a constant dividend barrier

Author

Listed:
  • Lili Zhang

Abstract

In this paper, the Erlang(n) risk model with two-sided jumps and a constant dividend barrier is considered. In the analysis of the expected discounted penalty function, the downward jumps are assumed to have an arbitrary distribution function and the upward jumps are assumed to be exponentially distributed. An integro-differential equation with boundary conditions for the expected discounted penalty function is derived and the solution is provided. The defective renewal equation for the expected discounted penalty function with no barrier is derived. In the analysis of the moments of the discounted dividend payments until ruin, we assume that the inter-jump times are generalized Erlang(n) distributed. An integro-differential equation for the mth moment function of the discounted sum of dividend payments until ruin is derived. Numerical examples are also given to obtain the expressions for the expected discounted penalty function and the expected present value of dividend payments.

Suggested Citation

  • Lili Zhang, 2021. "The Erlang(n) risk model with two-sided jumps and a constant dividend barrier," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(24), pages 5899-5917, November.
    • Handle: RePEc:taf:lstaxx:v:50:y:2021:i:24:p:5899-5917
    DOI: 10.1080/03610926.2020.1737712
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/03610926.2020.1737712
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/03610926.2020.1737712?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. Yue He & Reiichiro Kawai & Yasutaka Shimizu & Kazutoshi Yamazaki, 2022. "The Gerber-Shiu discounted penalty function: A review from practical perspectives," Papers 2203.10680, arXiv.org, revised Dec 2022.
    2. Jiaen Xu & Chunwei Wang & Naidan Deng & Shujing Wang, 2023. "Numerical Method for a Risk Model with Two-Sided Jumps and Proportional Investment," Mathematics, MDPI, vol. 11(7), pages 1-22, March.

    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:taf:lstaxx:v:50:y:2021:i:24:p:5899-5917. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/lsta .

    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.