Distortion function: Difference between revisions

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Revision as of 13:04, 25 January 2014

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{{Merge|Coherent risk measure|Distortion function|date=january 2014|section= General Framework of Wang Transform}}

{{context|date=May 2012}}

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"/>