IDEAS home Printed from https://ideas.repec.org/a/cup/astinb/v8y1975i03p284-290_01.html
   My bibliography  Save this article

Optimal Insurance Arrangements

Author

Listed:
  • Borch, Karl

Abstract

In a recent paper on the theory of demand for insurance Arrow [1] has proved that the optimal policy for an insurance buyer is one which gives complete coverage, beyond a fixed deductible. The result is proved under very general assumptions, but its content can be illustrated by the following simple example.Assume that a person is exposed to a risk which can cause him a loss x, represented by a stochastic variable with the distribution F(x). Assume further that he by paying the premium P(y) can obtain an insurance contract which will guarantee him a compensation y(x), if his loss amounts to x. The problem of our person is to find the optimal insurance contract, i.e. the optimal function y(x), when the price is given by the functional P(y).In order to give an operational formulation to the problem we have outlined, we shall assume that the person's attitude to risk can be represented by a Bernoulli utility function u(x), and we shall write S for his “initial wealth”. His problem will then be to maximizewhen the functional P(y) is given, and y(x) є Y. The set Y can be interpreted as the set of insurance policies available in the market. It is, natural to assume that o ≤ y(x) ≤ x, but beyond this there is no need for assuming additional restrictions on the set Y.

Suggested Citation

  • Borch, Karl, 1975. "Optimal Insurance Arrangements," ASTIN Bulletin, Cambridge University Press, vol. 8(3), pages 284-290, September.
    • Handle: RePEc:cup:astinb:v:8:y:1975:i:03:p:284-290_01
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S0515036100011223/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. Hong Mao & Krzysztof Ostaszewski, 2021. "Optimal Claim Settlement Strategies under Constraint of Cap on Claim Loss," Mathematics, MDPI, vol. 9(24), pages 1-12, December.
    2. Corina Constantinescu & Alexandra Dias & Bo Li & David Šiška & Simon Wang, 2022. "Effect of Stop-Loss Reinsurance on Primary Insurer Solvency," Risks, MDPI, vol. 10(10), pages 1-15, October.
    3. Kaluszka, Marek, 2004. "An extension of Arrow's result on optimality of a stop loss contract," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 527-536, December.
    4. Bakker, Frank M. & van Vliet, Rene C. J. A. & van de Ven, Wynand P. M. M., 2000. "Deductibles in health insurance: can the actuarially fair premium reduction exceed the deductible?," Health Policy, Elsevier, vol. 53(2), pages 123-141, September.
    5. Cheung, K.C. & Chong, W.F. & Yam, S.C.P., 2015. "The optimal insurance under disappointment theories," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 77-90.
    6. Elisa Luciano, 1999. "A Note on Loadings and Deductibles: Can a Vicious Circle Arise?," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 1999(2), pages 157-169.
    7. Burren, Daniel, 2013. "Insurance demand and welfare-maximizing risk capital—Some hints for the regulator in the case of exponential preferences and exponential claims," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 551-568.
    8. Wang, Shaun, 1996. "Ordering of risks under PH-transforms," Insurance: Mathematics and Economics, Elsevier, vol. 18(2), pages 109-114, July.
    9. Dutang, Christophe & Albrecher, Hansjoerg & Loisel, Stéphane, 2013. "Competition among non-life insurers under solvency constraints: A game-theoretic approach," European Journal of Operational Research, Elsevier, vol. 231(3), pages 702-711.
    10. José Daniel López-Barrientos & Ekaterina Viktorovna Gromova & Ekaterina Sergeevna Miroshnichenko, 2020. "Resource Exploitation in a Stochastic Horizon under Two Parametric Interpretations," Mathematics, MDPI, vol. 8(7), pages 1-29, July.
    11. Li, Wenyuan & Tan, Ken Seng & Wei, Pengyu, 2021. "Demand for non-life insurance under habit formation," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 38-54.
    12. Sung, K.C.J. & Yam, S.C.P. & Yung, S.P. & Zhou, J.H., 2011. "Behavioral optimal insurance," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 418-428.
    13. repec:hal:wpaper:hal-00746245 is not listed on IDEAS

    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:8:y:1975:i:03:p:284-290_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.