Distortion function

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A distortion function is a non-decreasing function such that and . The dual distortion function is .[1][2] Distortion functions are used to define distortion risk measures.[2]

Given a probability space , then for any random variable and any distortion function we can define a new probability measure such that for any it follows that



  1. ^ a b Balbás, A.; Garrido, J.; Mayoral, S. (2008). "Properties of Distortion Risk Measures". Methodology and Computing in Applied Probability. 11 (3): 385. doi:10.1007/s11009-008-9089-z. 
  2. ^ a b Julia L. Wirch; Mary R. Hardy. "Distortion Risk Measures: Coherence and Stochastic Dominance" (pdf). Retrieved March 10, 2012.