A new characterization of distortion premiums via countable additivity for comonotonic risks

For premium calculation principles or risk measures, all existing works only consider the additivity for a finite number of comonotonic risks. As we all know, a limiting status of finite additivity is the additivity for countable risks. In this paper we investigate the countable additivity and generate new and elegant characterizations for Choquet pricing and distortion premium principles. We also study the countable exchangeability, as an extension to additivity. It leads to generalized Choquet pricing and generalized distortion premium principles.