AxiomAn axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word ἀξίωμα (), meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'. The precise definition varies across fields of study. In classic philosophy, an axiom is a statement that is so evident or well-established, that it is accepted without controversy or question.
Distortion risk measureIn financial mathematics and economics, a distortion risk measure is a type of risk measure which is related to the cumulative distribution function of the return of a financial portfolio. The function associated with the distortion function is a distortion risk measure if for any random variable of gains (where is the Lp space) then where is the cumulative distribution function for and is the dual distortion function . If almost surely then is given by the Choquet integral, i.e.
