Non-differentiable transformations preserving stochastic dominance

Denuit, Michel;Eeckhoudt, Louis;Jokung, Octave
(2013) The journal of the Operational Research Society — Vol. 64, n° 9, p. 1441-1446 (2013)

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Authors
  • Denuit, MichelUCLouvain
    Author
  • Eeckhoudt, LouisUCLouvain
    Author
  • Jokung, OctaveBusiness School Lille-Nice, France
    Author
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.
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Denuit, M., Eeckhoudt, L., & Jokung, O. (2013). Non-differentiable transformations preserving stochastic dominance. The journal of the Operational Research Society, 64(9), 1441-1446. https://doi.org/10.1057/jors.2012.140 (Original work published 2013)