Puneet Varma (Editor)

Distortion function

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A distortion function 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 ) = 1 g ( 1 x ) . Distortion functions are used to define distortion risk measures.

Given a probability space ( Ω , F , P ) , then for any random variable X and any distortion function g we can define a new probability measure Q such that for any A F it follows that

Q ( A ) = g ( P ( X A ) ) .

References

Distortion function Wikipedia


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