Integral Representation of Continuous Comonotonically Additive Functionals

On Characterization of Distortion Premium Principle* By

In this paper, based on the additive measure integral representation of a nonadditive measure integral, it is shown that any comonotonically additive premium principle can be represented as an integral of the distorted decumulative distribution function of the insurance risk. Furthermore, a sufficient and necessary condition that a premium principle is a distortion premium principle is given.

GENERALIZED POSITIVE DEFINITE FUNCTIONS AND COMPLETELY MONOTONE FUNCTIONS ON FOUNDATION SEMIGROUPS

A general notion of completely monotone functionals on an ordered Banach algebra B into a proper H*-algebra A with an integral representation for such functionals is given. As an application of this result we have obtained a characterization for the generalized completely continuous monotone functions on weighted foundation semigroups. A generalized version of Bochner’s theorem on foundation se...

A Representation for Characteristic Functionals of Stable Random Measures with Values in Sazonov Spaces

Representation of increasing convex functionals with countably additive measures

We derive two types of representation results for increasing convex functionals in terms of countably additive measures. The first is a max-representation of functionals defined on spaces of realvalued continuous functions and the second a sup-representation of functionals defined on spaces of real-valued measurable functions. MSC 2010: 47H07, 28C05, 28C15

Characterization of a coherent upper conditional prevision as the Choquet integral with respect to its associated Hausdorff outer measure

A model of coherent upper conditional prevision for bounded random variables is proposed in a metric space. It is defined by the Choquet integral with respect to Hausdorff outer measure if the conditioning event has positive and finite Hausdorff outer measure in its Hausdorff dimension. Otherwise, when the conditioning event has Hausdorff outer measure equal to zero or infinity in its Hausdorff...