Marcus C. Christiansen
Institut f¨ur Versicherungswissenschaften
Universit¨at Ulm
D-89069 Ulm, Germany

Michel M. Denuit
Institut de Statistique, Biostatistique et Sciences Actuarielles
Universit´e Catholique de Louvain
B-1348 Louvain-la-Neuve, Belgium

Dorina Lazar
Faculty of Economics and Business Administration
Babes-Bolyai University
Cluj-Napoca, Romania

Abstract

In this paper, we develop a model supporting the so-called square-root formula used in Solvency II to aggregate the modular life SCR. Describing the insurance policy by a Markov jump process, we can obtain expressions similar to the square-root formula in Solvency II by means of limited expansions around the best estimate. Numerical illustrations are given, based on German population data. Even if the square-root formula can be supported by theoretical considerations, it is shown that the QIS correlation matrix is highly questionable.

http://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi/forschung/Prep...