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A '''distortion function''' <math>g: [0,1] \to [0,1]</math> is a [[non-decreasing function]] such that <math>g(0) = 0</math> and <math>g(1) = 1</math>. The '''dual distortion function''' is <math>\tilde{g}(x) = 1 - g(1-x)</math>.<ref name="PropertiesDRM">{{cite doi|10.1007/s11009-008-9089-z}}</ref><ref name="Wirch">{{cite web|title=Distortion Risk Measures: Coherence and Stochastic Dominance|author=Julia L. Wirch|author2=Mary R. Hardy|url=http://pascal.iseg.utl.pt/~cemapre/ime2002/main_page/papers/JuliaWirch.pdf|format=pdf|accessdate=March 10, 2012}}</ref> Distortion functions are used to define [[distortion risk measure]]s.<ref name="Wirch"/>
Given a [[probability space]] <math>(\Omega,\mathcal{F},\mathbb{P})</math>, then for any [[random variable]] <math>X</math> and any distortion function <math>g</math> we can define a new [[probability measure]] <math>\mathbb{Q}</math> such that for any <math>A \in \mathcal{F}</math> it follows that
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== References ==
{{Reflist}}
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