Distorted Probabilities and Bayesian Confirmation Measures

Bayesian Confirmation Measures (BCMs) assess the impact of the occurrence of one event on the credibility of another. Many mea- sures of this kind have been defined in literature. We want to analyze how these measures change when the probabilities involved in their computation are distorted. Composing distortions and BCMs we define a set of Distorted Bayesian Confirmation Measures (DBCMs); we study the properties that DBCMs may inherit from BCMs, and propose a way to measure the degree of distortion of a DBCM with respect to a corre- sponding BCM

On the Interplay between Distortion, Mean Value and Haezendonck-Goovaerts Risk Measures

In the actuarial research, distortion, mean value and Haezendonck-Goovaerts risk measures are concepts that are usually treated separately. In this paper we indicate and characterize the relation between these different risk measures, as well as their relation to convex risk measures. While it is known that the mean value principle can be used to generate premium calculation principles, we will show how they also allow to generate solvency calculation principles. Moreover, we explain the role provided for the distortion risk measures as an extension of the Tail Value-at-Risk (TVaR) and Conditional Tail Expectation (CTE)