Distortion function

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A distortion function in mathematics and statistics, for example, g:[0,1][0,1], is a non-decreasing function such that g(0)=0 and g(1)=1. The dual distortion function is g~(x)=1g(1x).[1][2] Distortion functions are used to define distortion risk measures.[2] Given a probability space (Ω,,), then for any random variable X and any distortion function g we can define a new probability measure such that for any A it follows that

(A)=g((XA)). [1]

References

  1. 1.0 1.1 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. hdl:10016/14071. S2CID 53327887.
  2. 2.0 2.1 Julia L. Wirch; Mary R. Hardy. "Distortion Risk Measures: Coherence and Stochastic Dominance" (PDF). Archived from the original (PDF) on July 5, 2016. Retrieved March 10, 2012.