IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v55y2014icp301-309.html
   My bibliography  Save this article

Improved asymptotic upper bounds on the ruin capital in the Lundberg model of risk

Author

Listed:
  • Malinovskii, Vsevolod K.

Abstract

This paper deals with ruin capital uα,t(c∣λ,μ) in the classical Lundberg model of risk. It is defined as the initial capital needed to keep the probability of ruin within finite time t equal to a predefined value α. Considered as a decreasing function of premium rate c, the ruin capital is shown to be convex (i.e., concave downward) for c>λ/μ and t sufficiently large. This observation is used to construct explicit upper bounds on the ruin capital.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:insuma:v:55:y:2014:i:c:p:301-309
    DOI: 10.1016/j.insmatheco.2013.12.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016766871400002X
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.insmatheco.2013.12.004?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.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Malinovskii, Vsevolod K., 2008. "Adaptive control strategies and dependence of finite time ruin on the premium loading," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 81-94, February.
    4. Malinovskii, Vsevolod K., 1998. "Non-Poissonian claims' arrivals and calculation of the probability of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 22(2), pages 123-138, June.
    5. Malinovskii, Vsevolod K., 2013. "Rationale of underwriters’ pricing conduct on competitive insurance market," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 325-333.
    6. Malinovskii, Vsevolod K., 2013. "Level premium rates as a function of initial capital," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 370-380.
    7. Malinovskii, Vsevolod K., 2008. "Risk theory insight into a zone-adaptive control strategy," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 656-667, April.
    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. 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.
    2. 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.
    3. 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., 2013. "Rationale of underwriters’ pricing conduct on competitive insurance market," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 325-333.
    6. Vsevolod Malinovskii, 2020. "Value-at-Risk substitute for non-ruin capital is fallacious and redundant," Papers 2005.05428, arXiv.org.
    7. Malinovskii, Vsevolod K., 2015. "On rational pricing for a profit-seeking insurer in the year of hard market," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 107-117.
    8. Willmot, Gordon E., 2007. "On the discounted penalty function in the renewal risk model with general interclaim times," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 17-31, July.
    9. Borovkov, Konstantin A. & Dickson, David C.M., 2008. "On the ruin time distribution for a Sparre Andersen process with exponential claim sizes," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1104-1108, June.
    10. Arthur Charpentier, 2010. "Reinsurance, ruin and solvency issues: some pitfalls," Working Papers hal-00463381, HAL.
    11. 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.
    12. Malinovskii, Vsevolod K., 2015. "Business planning for a profit-seeking insurer under deficiency of information," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 215-226.
    13. Landriault, David & Lemieux, Christiane & Willmot, Gordon E., 2012. "An adaptive premium policy with a Bayesian motivation in the classical risk model," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 370-378.
    14. Carol Thiago Costa & Wesley Vieirada Silva & Lauro Britode Almeida & Claudimar Pereirada Veiga, 2017. "Empirical evidence of the existence of speculative bubbles in the prices of stocks traded on the São Paulo Stock Exchange," Contaduría y Administración, Accounting and Management, vol. 62(4), pages 1317-1334, Octubre-D.
    15. Malinovskii, Vsevolod K., 2008. "Adaptive control strategies and dependence of finite time ruin on the premium loading," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 81-94, February.

    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:eee:insuma:v:55:y:2014:i:c:p:301-309. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    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.