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The Utility Concept Applied to the Theory of Insurance

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  • Borch, Karl

Abstract

In some recent papers ((1), (2) and (3)) about reinsurance problems I have made extensive use of utility concepts. It has been shown that if a company follows well defined objectives in its reinsurance policy, these objectives can be represented by a utility function which the company seeks to maximise. This formulation of the problem will in general make it possible to determine a unique reinsurance arrangement which is optimal when the company's objectives and external situation are given.More than 50 years ago Guldberg (4) wrote (about the probability of ruin): “Wie hoch diese Wahrscheinlichkeit gegriffen werden soil, muss dent subjektiven Ermessen oder von Aussen kommenden Bedingungen überlassen bleiben”. This is the traditional approach to reinsurance problems. It does obviously not lead to a determinate solution. Most authors taking this approach conclude their studies by giving a mathematical relation between some measure of “stability”, such as the probability of ruin, and some parameter, for instance maximum retention, to which the company can give any value within a certain range. Such studies do usually not state which particular value the company should select for this parameter, i.e. what degree of stability it should settle for. This question is apparently considered as being outside the field of actuarial mathematics.

Suggested Citation

  • Borch, Karl, 1961. "The Utility Concept Applied to the Theory of Insurance," ASTIN Bulletin, Cambridge University Press, vol. 1(5), pages 245-255, July.
    • Handle: RePEc:cup:astinb:v:1:y:1961:i:05:p:245-255_00
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    Cited by:

    1. Jhonni Sinaga & Adler Haymans Manurung & Nera Marinda Machdar & John Edward Harly Jacob FoEh, 2023. "Internal and External Determinants of Risk Based Capital," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 13(2), pages 1-5.
    2. Dionne, Georges & Harrington, Scott, 2017. "Insurance and Insurance Markets," Working Papers 17-2, HEC Montreal, Canada Research Chair in Risk Management.
    3. Jason S. Anquandah & Leonid V. Bogachev, 2019. "Optimal Stopping and Utility in a Simple Model of Unemployment Insurance," Papers 1902.06175, arXiv.org, revised Sep 2019.
    4. Alexandra Moura & Carlos Oliveira, 2024. "Reputation risk mitigation in investment strategies," Working Papers REM 2024/0309, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    5. Timmermans, S. & Schumacher, J.M. & Ponds, E.H.M., 2011. "A Cohort-Specific Approach to Retirement Savings," Other publications TiSEM 9f3040ab-8dd3-4eeb-b45a-6, Tilburg University, School of Economics and Management.
    6. Aleksandar Arandjelovi'c & Julia Eisenberg, 2024. "Reinsurance with neural networks," Papers 2408.06168, arXiv.org.
    7. Wang, S., 1994. "Premium Calculation by Transforming the Layer Premium Density," Working Papers 030, Risk and Insurance Archive.
    8. Denuit, Michel & Vylder, Etienne De & Lefevre, Claude, 1999. "Extremal generators and extremal distributions for the continuous s-convex stochastic orderings," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 201-217, May.
    9. Jong-Hag Jang, 2018. "An Empirical Analysis of the Property Catastrophe Reinsurance," International Business Research, Canadian Center of Science and Education, vol. 11(1), pages 170-183, January.
    10. Debora Daniela Escobar & Georg Ch. Pflug, 2020. "The distortion principle for insurance pricing: properties, identification and robustness," Annals of Operations Research, Springer, vol. 292(2), pages 771-794, September.
    11. Alejandro Drexler & Richard Rosen, 2022. "Exposure to catastrophe risk and use of reinsurance: an empirical evaluation for the U.S," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 47(1), pages 103-124, January.
    12. Wang, Shaun, 1996. "Ordering of risks under PH-transforms," Insurance: Mathematics and Economics, Elsevier, vol. 18(2), pages 109-114, July.
    13. Jason S. Anquandah & Leonid V. Bogachev, 2019. "Optimal Stopping and Utility in a Simple Modelof Unemployment Insurance," Risks, MDPI, vol. 7(3), pages 1-41, September.
    14. Daniela Escobar & Georg Pflug, 2018. "The distortion principle for insurance pricing: properties, identification and robustness," Papers 1809.06592, arXiv.org.

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