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What was fair in acturial fairness?


  • Antonio José Heras Martínez

    () (Departamento de Economía Financiera y Contabilidad 1 - UCM - Universidad Complutense de Madrid [Madrid])

  • David Teira

    () (Departamento de Lógica, Historia y Filosofía de la ciencia - UNED - Universidad Nacional de Educación a Distancia)

  • Pierre-Charles Pradier

    () (CES - Centre d'économie de la Sorbonne - CNRS - Centre National de la Recherche Scientifique - UP1 - Université Panthéon-Sorbonne, Labex ReFi - UP1 - Université Panthéon-Sorbonne)


The concept of acturial fairness stems from an Aristotelian tradition in which fairness requires equality between the goods exchanged. When dealing with aleatory contracts, this principle evolved, among medieval scholars, into equality in risk: benefits and losses should be proportional to the risks undertaken. The formalization of this principle gave rise to the concept of mathematical expectation, first implemented in the calculation of the fair price of gambles. The concept of an actuarial fair price was first theoretically articulated in the 17th century as an implementation of this same Aristotelian principle in the field of life insurance. For a practical estimation of fair actuarial prices it was necessary to build mortality tables, assuming that the major risk factor was age. Yet, in the 18th and 19th centuries, we find no agreement among proto-actuaries about the proper construction of these tables. Among the obstacles they found, we want to highlight their early awareness of the possibility of adverse selection: buyers and sellers could manipulate the risk assessment for their own private interests, in a way that would either make fair companies collapse or fair customers be cheated. The paradox in the concept of actuarial fairness is that as soon as it was formally articulated, markets made clear it could never be implemented in actual pricing.

Suggested Citation

  • Antonio José Heras Martínez & David Teira & Pierre-Charles Pradier, 2016. "What was fair in acturial fairness?," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01400213, HAL.
  • Handle: RePEc:hal:cesptp:halshs-01400213
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    References listed on IDEAS

    1. Xavier Landes, 2015. "How Fair Is Actuarial Fairness?," Journal of Business Ethics, Springer, vol. 128(3), pages 519-533, May.
    2. David R. Bellhouse, 2011. "A new look at Halley's life table," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 174(3), pages 823-832, July.
    3. Georges Gallais-Hamonno & Christian Rietsch, 2003. "Essai sur les probabilités de la durée de la vie humaine (1746), Antoine Deparcieux," Post-Print halshs-00256030, HAL.
    4. Arthur Charpentier & Michel M. Denuit & Romuald Elie, 2015. "Segmentation et mutualisation, les deux faces d'une même pièce?," Post-Print halshs-01242561, HAL.
    5. Timothy Johnson, 2015. "Reciprocity as a Foundation of Financial Economics," Journal of Business Ethics, Springer, vol. 131(1), pages 43-67, September.
    6. Pierre-Charles Pradier, 2016. "The debt of the Hôtel-Dieu de Paris from 1660 to 1690: a testbed for sovereign default," Documents de travail du Centre d'Economie de la Sorbonne 16057, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    7. Edith Dudley Sylla, 2003. "Business Ethics, Commercial Mathematics, and the Origins of Mathematical Probability," History of Political Economy, Duke University Press, vol. 35(5), pages 309-337, Supplemen.
    8. Turo-Kimmo Lehtonen & Jyri Liukko, 2011. "The Forms and Limits of Insurance Solidarity," Journal of Business Ethics, Springer, vol. 103(1), pages 33-44, April.
    9. Geoffrey Poitras, 2000. "The Early History of Financial Economics, 1478–1776," Books, Edward Elgar Publishing, number 2151.
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    More about this item


    actuarial fairness; mathematical expectation; life insurance; annuity; risk; rente; assurance-vie; justice actuarielle; espérance mathématique; risque;

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation
    • G01 - Financial Economics - - General - - - Financial Crises

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