Abstract

Autocalibration is a desirable property, intimately related to the method of marginal totals that predates modern risk classification methods. Autocalibrated mean predictors π for a response Y and feature variables X are such that π(X) =E[Y |π(X)]. Autocalibration is beneficial since it ensures that the information contained in π is used without any systematic errors. Or stated differently, an autocalibrated predictor is optimal with respect to the information contained in it. Autocalibration can easily be implemented using the practical method proposed by Denuit, Charpentier and Trufin (2021), consisting in an extra local regression step. Professional practice favors Lorenz curves and Gini coefficients to assess the performances of a candidate premium. Under autocalibration, Denuit and Trufin (2021) established that the advanced diagnostic tools proposed by Denuit, Sznajder and Trufin (2019) reduce to Lorenz curve and Gini coefficients, respectively. The present note aims to assess the impact of autocalibration on the goodness of lift. Lift graphs compare average predicted and average actual loss costs when policies have been ranked according to the candidate premium and grouped within buckets. It is shown on a case study that autocalibration does not only restore global and local balances but also improve lift.

Keywords: Risk classification, Ratemaking, Lift curve, Goodness of lift, Machine learning.

Sector: Insurance

Expertise: Autocalibration

Authors: Nicolas Ciatto,

Harrison Verelst,

Michel Denuit, and Julien Trufin

Publisher: Detralytics

Date: July 2022

Language: English

Pages: 17

Reference : FAQctuary 2022-2

About the authors

Nicolas Ciatto

Nicolas fait partie du Talent Consolidation Program (TCP) et occupe également la fonction de People Lead chez Detralytics. Avant de rejoindre l’entreprise, il a effectué un stage actuariel chez Axa Belgium, au sein du département Non-Vie. Fort d’une solide expertise en assurance Non-Vie et en tarification, il a travaillé sur la mise en œuvre de méthodes Non-Vie dans le cadre de la tarification a priori et a posteriori, en utilisant R.

Harrison Verelst

Harrison was part of the Talent Consolidation Program (TCP) at the time of the publication. He holds two Master’s degrees in Mechanical Engineering and Quantitative Finance as well as a Master’s in actuarial sciences from ULB.

Michel Denuit

Michel Denuit

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 Trufin

Julien Trufin

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.