Non-differentiable transformations preserving stochastic dominance

M Denuit, Louis Eeckhoudt and O Jokung
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M Denuit: Institut de Statistique, Biostatistique & Sciences Actuarielles, Université Catholique de Louvain, Louvain-la-Neuve, Belgium
O Jokung: EDHEC Business School Lille-Nice, Lille, France

Journal of the Operational Research Society, 2013, vol. 64, issue 9, 1441-1446

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.

Date: 2013
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