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Projection models for health expenses

Published online by Cambridge University Press:  18 December 2017

Marcus Christiansen*
Institute for Mathematics, University of Oldenburg, Carl von Ossietzky Straβe 9-11, D-26111, Oldenburg, Germany
Michel Denuit
Institute of Statistics, Biostatistics and Actuarial Science, Université Catholique de Louvain (UCL), Voie du Roman Pays 20/L1.04.01, B-1348, Louvain-la-Neuve, Belgium
Nathalie Lucas
Institute of Statistics, Biostatistics and Actuarial Science, Université Catholique de Louvain (UCL), Voie du Roman Pays 20/L1.04.01, B-1348, Louvain-la-Neuve, Belgium
Jan-Philipp Schmidt
Institute for Insurance Studies (ivwKöln), TH Köln – University of Applied Sciences, Gustav-Heinemann-Ufer 54, D-50968 Köln, Cologne, Germany
*Correspondence to: Marcus Christiansen, Institute for Mathematics, University of Oldenburg, Oldenburg, Germany. E-mail:


This note proposes a practical way for modelling and projecting health insurance expenditures over short time horizons, based on observed historical data. The present study is motivated by a similar age structure generally observed for health insurance claim frequencies and yearly aggregate losses on the one hand and mortality on the other hand. As an application, the approach is illustrated for German historical inpatient costs provided by the Federal Financial Supervisory Authority. In particular, similarities and differences to mortality modelling are addressed.

© Institute and Faculty of Actuaries 2017 

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