IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v2y2014i3p249-259d37899.html
   My bibliography  Save this article

Elementary Bounds on the Ruin Capital in a Diffusion Model of Risk

Author

Listed:
  • Vsevolod K. Malinovskii

    (Central Economics and Mathematics Institute (CEMI) of Russian Academy of Science, Nakhimovskiy prosp., 47, Moscow 117418, Russia)

Abstract

In a diffusion model of risk, we focus on the initial capital needed to make the probability of ruin within finite time equal to a prescribed value. It is defined as a solution of a nonlinear equation. The endeavor to write down and to investigate analytically this solution as a function of the premium rate seems not technically feasible. Instead, we obtain informative bounds for this capital in terms of elementary functions.

Suggested Citation

  • Vsevolod K. Malinovskii, 2014. "Elementary Bounds on the Ruin Capital in a Diffusion Model of Risk," Risks, MDPI, vol. 2(3), pages 1-11, July.
    • Handle: RePEc:gam:jrisks:v:2:y:2014:i:3:p:249-259:d:37899
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/2/3/249/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-9091/2/3/249/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Malinovskii, Vsevolod K., 2014. "Improved asymptotic upper bounds on the ruin capital in the Lundberg model of risk," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 301-309.
    2. Malinovskii, V. K., 2007. "Zone-Adaptive Control Strategy for a Multiperiodic Model of Risk," Annals of Actuarial Science, Cambridge University Press, vol. 2(2), pages 349-367, September.
    3. Malinovskii, Vsevolod K., 2009. "Scenario Analysis for a Multi-Period Diffusion Model of Risk," ASTIN Bulletin, Cambridge University Press, vol. 39(2), pages 649-676, November.
    4. Malinovskii, Vsevolod K., 2013. "Level premium rates as a function of initial capital," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 370-380.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Malinovskii, Vsevolod K. & Kosova, Ksenia O., 2014. "Simulation analysis of ruin capital in Sparre Andersen’s model of risk," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 184-193.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Malinovskii, Vsevolod K., 2014. "Annual intrinsic value of a company in a competitive insurance market," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 310-318.
    2. Malinovskii, Vsevolod K. & Kosova, Ksenia O., 2014. "Simulation analysis of ruin capital in Sparre Andersen’s model of risk," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 184-193.
    3. Malinovskii, Vsevolod K., 2013. "Level premium rates as a function of initial capital," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 370-380.
    4. Malinovskii, Vsevolod K., 2012. "Equitable solvent controls in a multi-period game model of risk," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 599-616.
    5. Malinovskii, Vsevolod K., 2014. "Improved asymptotic upper bounds on the ruin capital in the Lundberg model of risk," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 301-309.
    6. Malinovskii, Vsevolod K., 2013. "Rationale of underwriters’ pricing conduct on competitive insurance market," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 325-333.

    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:gam:jrisks:v:2:y:2014:i:3:p:249-259:d:37899. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc 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 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.