In order to determine an appropriate amount of premium, statistical goodness-of-fit criteria must be supplemented with actuarial ones when assessing performance of a given candidate pure premium. In this paper, concentration curves and Lorenz curves are shown to provide actuaries with effective tools to evaluate whether a premium is appropriate or to compare two competing alternatives. The idea is to compare the premium income for sub-portfolios gathering low risks (identified as low by means of the premiums under consideration) to the true one, or equivalently, to the actual losses. Numerical illustrations performed on hypothetical data and real ones demonstrate the usefulness of the proposed approach.
Sector: Insurance
Authors: Dominic Sznajder,
Michel Denuit, Julien Trufin
Publication : Insurance Mathematics
and Economics
Date: March 2019
Language: English
Michel est Conseiller Scientifique Honoraire chez Detralytics, ainsi que professeur en sciences actuarielles à l’Université Catholique de Louvain. Il dispose d’une expérience internationale en tant que professeur invité et a initié de nombreux projets en collaboration avec l’industrie. Au sein de Detralytics, Michel accompagne les jeunes talents, dispense des formations de pointe, stimule l’innovation et supervise des projets de R&D.
Julien est Scientific Advisor chez Detralytics et Professeur en sciences actuarielles au sein du département de mathématiques de l’Université Libre de Bruxelles. Il possède une expérience en tant que consultant et un solide parcours académique développé au sein d’institutions de renom, dont l’Université Laval (Canada), l’UCL et l’ULB (Belgique). Chez Detralytics, Julien encadre les jeunes talents, dispense des formations de pointe, stimule l’innovation et supervise les projets de R&D.
Dominik Sznajder obtained a master degree in Economics and in Mathematics at Warsaw University in 2007. Thereafter he completed a PhD programme at KU Leuven in the section of Mathematical Statistics in 2011. Dominik was a visiting lecturer at UGent in 2013 and an FWO post-doctoral researcher before transferring to business. He worked as an actuarial consultant with Milliman supporting insurance companies in the Benelux region. Currently he is a freelance Data Scientist, Actuarial & Financial Modeler, while also doing research at KU Leuven. Dominik has over 10 years of experience in using R, when he developed R based solutions both in Business and Academia.
