IDEAS home Printed from https://ideas.repec.org/a/taf/sactxx/v2014y2014i2p93-115.html
   My bibliography  Save this article

A generalised Gerber–Shiu measure for Markov-additive risk processes with phase-type claims and capital injections

Author

Listed:
  • Lothar Breuer
  • Andrei Badescu

Abstract

In this paper we consider a risk reserve process where the arrivals (either claims or capital injections) occur according to a Markovian point process. Both claim and capital injection sizes are phase-type distributed and the model allows for possible correlations between these and the inter-claim times. The premium income is modelled by a Markov-modulated Brownian motion which may depend on the underlying phases of the point arrival process. For this risk reserve model we derive a generalised Gerber–Shiu measure that is the joint distribution of the time to ruin, the surplus immediately before ruin, the deficit at ruin, the minimal risk reserve before ruin, and the time until this minimum is attained. Numeral examples illustrate the influence of the parameters on selected marginal distributions.

Suggested Citation

  • Lothar Breuer & Andrei Badescu, 2014. "A generalised Gerber–Shiu measure for Markov-additive risk processes with phase-type claims and capital injections," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2014(2), pages 93-115.
    • Handle: RePEc:taf:sactxx:v:2014:y:2014:i:2:p:93-115
    DOI: 10.1080/03461238.2011.636969
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/03461238.2011.636969
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/03461238.2011.636969?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.

    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:sactxx:v:2014:y:2014:i:2:p:93-115. 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/sact .

    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.