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).