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Non-differentiable transformations preserving stochastic dominance

Author

Listed:
  • M Denuit

    (Institut de Statistique, Biostatistique & Sciences Actuarielles, Université Catholique de Louvain, Louvain-la-Neuve, Belgium)

  • L Eeckhoudt

    (1] IESEG School of Management, LEM, Lille, France[2] CORE, Université Catholique de Louvain, Louvain-la-Neuve, Belgium)

  • O Jokung

    (EDHEC Business School Lille-Nice, Lille, France)

Abstract

In this paper, we solve the following problem: when does a stochastic improvement in one risk maintain itself under a non everywhere continuously differentiable transformation of this risk? Using the notion of divided differences, we show that stochastic dominance at the third (and higher) order, and sometimes at the second one, is not preserved after simple piecewise linear transformation of the initial risk. Our analysis complements the one that exists for everywhere continuously differentiable transformations.

Suggested Citation

  • M Denuit & L Eeckhoudt & O Jokung, 2013. "Non-differentiable transformations preserving stochastic dominance," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 64(9), pages 1441-1446, September.
    • Handle: RePEc:pal:jorsoc:v:64:y:2013:i:9:p:1441-1446
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    References listed on IDEAS

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    Cited by:

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    3. Gollier, Christian, 2021. "A general theory of risk apportionment," Journal of Economic Theory, Elsevier, vol. 192(C).

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