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The Utility Concept Applied to the Theory of Insurance


  • Borch, Karl


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. Jason S. Anquandah & Leonid V. Bogachev, 2019. "Optimal Stopping and Utility in a Simple Model of Unemployment Insurance," Papers 1902.06175,, revised Sep 2019.
    2. Wang, Shaun, 1996. "Ordering of risks under PH-transforms," Insurance: Mathematics and Economics, Elsevier, vol. 18(2), pages 109-114, July.
    3. Jason S. Anquandah & Leonid V. Bogachev, 2019. "Optimal Stopping and Utility in a Simple Modelof Unemployment Insurance," Risks, MDPI, Open Access Journal, vol. 7(3), pages 1-41, September.
    4. Wang, S., 1994. "Premium Calculation by Transforming the Layer Premium Density," Working Papers 030, Risk and Insurance Archive.
    5. Daniela Escobar & Georg Pflug, 2018. "The distortion principle for insurance pricing: properties, identification and robustness," Papers 1809.06592,
    6. 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.
    7. Dionne, Georges & Harrington, Scott, 2017. "Insurance and Insurance Markets," Working Papers 17-2, HEC Montreal, Canada Research Chair in Risk Management.
    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.

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