IDEAS home Printed from https://ideas.repec.org/a/cup/astinb/v6y1971i02p147-152_01.html
   My bibliography  Save this article

Exemplification of Ruin Probabilities

Author

Listed:
  • Wikstad, Nils

Abstract

The following numerical values of ruin probabilities, Ψ(u, T) for finite times T, have been calculated by the method proposed in “Analytical steps towards a numerical calculation of the ruin probability for a finite period when the risk process is of the Poisson type or of the more general type studied by Sparre Andersen”, presented to this colloquium by Olof Thorin. The notations used in the sequel follow those of Thorin.Two distributions of the individual claims are considered, viz.,The latter distribution is a rather crude attempt to interprete the extremely skew distribution (Swedish non-industry fire insurance 1948-1951) considered by Cramér in his treatise “Collective Risk Theory”, Jubilee volume of Försäkringsaktiebolaget Skandia (1955) pp. 43-45.Likewise two distributions of the interoccurence times are considered, viz.,The d.f.B was considered by Sparre Andersen (TICA 1957 vol. II pp. 225-227).Note that the first moment equals one in all the d.f. mentioned.Though the analytical machinery also seems to work for o ≤ c ≤ 1 the Ψ values are indicated only for some values of c > 1. As known from Thorin's paper c stands for 1 + λ, where λ is the premiumloading, which means that for c = o Ψ(u, T) corresponds to the tail of the d.f. for the total amount of claims during the period (o, T).

Suggested Citation

  • Wikstad, Nils, 1971. "Exemplification of Ruin Probabilities," ASTIN Bulletin, Cambridge University Press, vol. 6(2), pages 147-152, December.
  • Handle: RePEc:cup:astinb:v:6:y:1971:i:02:p:147-152_01
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S0515036100010874/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. Mehmet Akif Yazici & Nail Akar, 2017. "The finite/infinite horizon ruin problem with multi-threshold premiums: a Markov fluid queue approach," Annals of Operations Research, Springer, vol. 252(1), pages 85-99, May.
    2. Grandell, Jan, 2000. "Simple approximations of ruin probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 157-173, May.
    3. Usabel, M. A., 1999. "Practical approximations for multivariate characteristics of risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 25(3), pages 397-413, December.
    4. Pawel Mista, 2006. "Analytical and numerical approach to corporate operational risk modelling," HSC Research Reports HSC/06/03, Hugo Steinhaus Center, Wroclaw University of Technology.
    5. Li Qin & Susan M. Pitts, 2012. "Nonparametric Estimation of the Finite-Time Survival Probability with Zero Initial Capital in the Classical Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 919-936, December.
    6. De Vylder, F. Etienne & Goovaerts, Marc J., 1999. "Explicit finite-time and infinite-time ruin probabilities in the continuous case," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 155-172, May.
    7. Usabel, Miguel, 1999. "Calculating multivariate ruin probabilities via Gaver-Stehfest inversion technique," Insurance: Mathematics and Economics, Elsevier, vol. 25(2), pages 133-142, November.
    8. Gyllenberg, Mats & S. Silvestrov, Dmitrii, 2000. "Cramer-Lundberg approximation for nonlinearly perturbed risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 26(1), pages 75-90, February.
    9. Yuguang Fan & Philip S. Griffin & Ross Maller & Alexander Szimayer & Tiandong Wang, 2017. "The Effects of Largest Claim and Excess of Loss Reinsurance on a Company’s Ruin Time and Valuation," Risks, MDPI, vol. 5(1), pages 1-27, January.

    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:6:y:1971:i:02:p:147-152_01. 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.