TY - JOUR
T1 - Clustering-Based Extensions of the Common Age Effect Multi-Population Mortality Model
AU - Schnürch, Simon
AU - Kleinow, Torsten
AU - Korn, Ralf
N1 - Funding Information:
Funding: S.S. is grateful for the financial support from the Fraunhofer Institute for Industrial Mathematics ITWM. T.K. acknowledges financial support from the Actuarial Research Centre of the Institute and Faculty of Actuaries through the research programme on “Modelling, Measurement and Management of Longevity and Morbidity Risk”.
Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2021/3/1
Y1 - 2021/3/1
N2 - We introduce four variants of the common age effect model proposed by Kleinow, which describes the mortality rates of multiple populations. Our model extensions are based on the assumption of multiple common age effects, each of which is shared only by a subgroup of all considered populations. This makes the models more realistic while still keeping them as parsimonious as possible, improving the goodness of fit. We apply different clustering methods to identify suitable subgroups. Some of the algorithms are borrowed from the unsupervised learning literature, while others are more domain-specific. In particular, we propose and investigate a new model with fuzzy clustering, in which each population’s individual age effect is a linear combination of a small number of age effects. Due to their good interpretability, our clustering-based models also allow some insights in the historical mortality dynamics of the populations. Numerical results and graphical illustrations of the considered models and their performance in-sample as well as out-of-sample are provided.
AB - We introduce four variants of the common age effect model proposed by Kleinow, which describes the mortality rates of multiple populations. Our model extensions are based on the assumption of multiple common age effects, each of which is shared only by a subgroup of all considered populations. This makes the models more realistic while still keeping them as parsimonious as possible, improving the goodness of fit. We apply different clustering methods to identify suitable subgroups. Some of the algorithms are borrowed from the unsupervised learning literature, while others are more domain-specific. In particular, we propose and investigate a new model with fuzzy clustering, in which each population’s individual age effect is a linear combination of a small number of age effects. Due to their good interpretability, our clustering-based models also allow some insights in the historical mortality dynamics of the populations. Numerical results and graphical illustrations of the considered models and their performance in-sample as well as out-of-sample are provided.
KW - Cluster analysis
KW - Common age effect model
KW - Maximum likelihood estimation
KW - Mortality modeling and forecasting
KW - Mortality of multiple populations
KW - Stochastic mortality model
UR - http://www.scopus.com/inward/record.url?scp=85102774847&partnerID=8YFLogxK
U2 - 10.3390/risks9030045
DO - 10.3390/risks9030045
M3 - Article
SN - 2227-9091
VL - 9
JO - Risks
JF - Risks
IS - 3
M1 - 45
ER -