Abstract
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
About the authors
Michel Denuit
Michel is an Honorary Scientific Advisor at Detralytics, as well as a professor in actuarial science at the Université Catholique de Louvain. He has international experience as a visiting professor, and has promoted many projects in collaboration with the industry. At Detralytics, Michel coaches young talents, provides cutting-edge training, fosters innovation and oversees R&D projects.
Julien Trufin
Julien is a Scientific Advisor at Detralytics, as well as a professor in Actuarial Science at the department of mathematics of the Université Libre de Bruxelles. Julien has experience as a consultant and a strong academic background developed at prominent institutions, including Université Laval (Canada), UCL, and ULB (Belgium). At Detralytics, Julien coaches young talents, provide cutting-edge training, fosters innovation and oversees R&D projects.
Dominik Sznajder
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.
