Content deleted Content added
Removing stale merge proposal from January 2014; no case made, no discussion over more than 3 years, case is not obvious |
Citation bot (talk | contribs) m Removed parameters. | You can use this bot yourself. Report bugs here. | User-activated. |
||
Line 1:
{{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 journal | last1 = Balbás | first1 = A. | last2 = Garrido | first2 = J. | last3 = Mayoral | first3 = S. | doi = 10.1007/s11009-008-9089-z | title = Properties of Distortion Risk Measures | journal = Methodology and Computing in Applied Probability | volume = 11 | issue = 3 | pages = 385 | year = 2008 | pmid = | pmc = }}</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.
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
| |||