Advanced Search
MyIDEAS: Login to save this article or follow this journal

An operator-based approach to the analysis of ruin-related quantities in jump diffusion risk models


Author Info

  • Feng, Runhuan
Registered author(s):


    Recent developments in ruin theory have seen the growing popularity of jump diffusion processes in modeling an insurer's assets and liabilities. Despite the variations of technique, the analysis of ruin-related quantities mostly relies on solutions to certain differential equations. In this paper, we propose in the context of Lévy-type jump diffusion risk models a solution method to a general class of ruin-related quantities. Then we present a novel operator-based approach to solving a particular type of integro-differential equations. Explicit expressions for resolvent densities for jump diffusion processes killed on exit below zero are obtained as by-products of this work.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 48 (2011)
    Issue (Month): 2 (March)
    Pages: 304-313

    as in new window
    Handle: RePEc:eee:insuma:v:48:y:2011:i:2:p:304-313

    Contact details of provider:
    Web page:

    Related research

    Keywords: Jump diffusion process Ruin theory Expected discounted penalty at ruin Integro-differential equation Operator calculus Resolvent density;


    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    1. Feng, Runhuan, 2009. "On the total operating costs up to default in a renewal risk model," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 45(2), pages 305-314, October.
    2. Bjarne Højgaard & Michael Taksar, 2001. "Optimal risk control for a large corporation in the presence of returns on investments," Finance and Stochastics, Springer, Springer, vol. 5(4), pages 527-547.
    3. Gerber, Hans U. & Landry, Bruno, 1998. "On the discounted penalty at ruin in a jump-diffusion and the perpetual put option," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 22(3), pages 263-276, July.
    4. Jang, Jiwook, 2007. "Jump diffusion processes and their applications in insurance and finance," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 41(1), pages 62-70, July.
    5. Lin, X. Sheldon & Willmot, Gordon E., 1999. "Analysis of a defective renewal equation arising in ruin theory," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 25(1), pages 63-84, September.
    6. Wang, Guojing & Wu, Rong, 2000. "Some distributions for classical risk process that is perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 26(1), pages 15-24, February.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:
    1. Cheung, Eric C.K. & Feng, Runhuan, 2013. "A unified analysis of claim costs up to ruin in a Markovian arrival risk model," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 53(1), pages 98-109.
    2. Feng, Runhuan & Volkmer, Hans W., 2012. "Modeling credit value adjustment with downgrade-triggered termination clause using a ruin theoretic approach," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 51(2), pages 409-421.


    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.


    Access and download statistics


    When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:48:y:2011:i:2:p:304-313. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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