IDEAS home Printed from https://ideas.repec.org/a/cup/astinb/v21y1991i01p133-146_00.html
   My bibliography  Save this article

The Schmitter Problem and a Related Problem: A Partial Solution

Author

Listed:
  • Kaas, R.

Abstract

At the 1990 ASTIN-colloquium, Schmitter posed the problem of finding the extreme values of the ultimate ruin probability ψ(u) in a risk process with initial capital u, fixed safety margin θ, and mean μ and variance σ2 of the individual claims. This note aims to give some more insight into this problem. Schmitter's conjecture that the maximizing individual claims distribution is always diatomic is disproved by a counterexample. It is shown that if one uses the distribution maximizing the upper bound e−Ru to find a ‘large’ ruin probability among risks with range [0, b], incorrect results are found if b is large or u small. The related problem of finding extreme values of stop-loss premiums for a compound Poisson (λ) distribution with identical restrictions on the individual claims is analyzed by the same methods. The results obtained are very similar.

Suggested Citation

  • Kaas, R., 1991. "The Schmitter Problem and a Related Problem: A Partial Solution," ASTIN Bulletin, Cambridge University Press, vol. 21(1), pages 133-146, April.
  • Handle: RePEc:cup:astinb:v:21:y:1991:i:01:p:133-146_00
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S0515036100004414/type/journal_article
    File Function: link to article abstract page
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. De Vylder, F. & Goovaerts, M. & Marceau, E., 1997. "The bi-atomic uniform minimal solution of Schmitter's problem," Insurance: Mathematics and Economics, Elsevier, vol. 20(1), pages 59-78, June.
    2. De Vylder, F. & Marceau, E., 1996. "The numerical solution of the Schmitter problems: Theory," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 1-18, December.
    3. Hansjörg Albrecher & José Carlos Araujo-Acuna, 2022. "On The Randomized Schmitter Problem," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 515-535, June.
    4. De Vylder, F. & Goovaerts, M. & Marceau, E., 1997. "The solution of Schmitter's simple problem: Numerical illustration," Insurance: Mathematics and Economics, Elsevier, vol. 20(1), pages 43-58, June.

    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:cup:astinb:v:21:y:1991:i:01:p:133-146_00. 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: Kirk Stebbing (email available below). General contact details of provider: https://www.cambridge.org/asb .

    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.