Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-08T21:33:25.075Z Has data issue: false hasContentIssue false
  • English
  • Français

LIFELONG HEALTH INSURANCE COVERS WITH SURRENDER VALUES: UPDATING MECHANISMS IN THE PRESENCE OF MEDICAL INFLATION

Published online by Cambridge University Press:  15 June 2017

Jan Dhaene ,
Els Godecharle ,
Katrien Antonio ,
Michel Denuit  and
Hamza Hanbali
Jan Dhaene
Affiliation:
Faculty of Economics and Business, KU Leuven, Belgium E-Mail: [email protected]
Els Godecharle
Affiliation:
Faculty of Economics and Business, KU Leuven, Belgium E-Mail: [email protected]
Katrien Antonio*
Affiliation:
Faculty of Economics and Business, KU Leuven, Belgium, Faculty of Economics and Business, University of Amsterdam, The Netherlands
Michel Denuit
Affiliation:
Institut de Statistique, Biostatistique et Sciences Actuarielles, Université Catholique de Louvain, Louvain-la-Neuve, Belgium E-Mail: [email protected]
Hamza Hanbali
Affiliation:
Faculty of Economics and Business, KU Leuven, Belgium E-Mail: [email protected]
*
E-Mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper considers the problem of a lifelong health insurance cover where medical inflation is not sufficiently incorporated in the level premium determined at policy issue. We focus on the setting where changes in health benefits, driven by medical inflation, are accounted for by an appropriate update or indexation of the level premium, the policy value, or both premium and policy value, during the term of the contract. Such an updating mechanism is necessary to restore the actuarial equivalence between future health benefits and surrender values on the one hand, and available policy values and future premiums on the other hand. We extend existing literature (Vercruysse et al., 2013; Denuit et al., 2017) by developing updating mechanisms in a discrete-time framework, where medical inflation is only taken into account ex-post as it emerges over time and where surrender values are allowed for. We propose and design two types of surrender values: based on the ageing provision on the one hand and based directly on the premiums paid until surrender on the other hand. We illustrate our updating strategy with numerical examples, using Belgian data, and investigate the sensitivity of our findings with respect to elements from the technical basis (in particular: the lapse rates) used in the actuarial calculations. Our updating mechanism is generic and useful for a wide range of products in life and health insurance, where some elements of the technical basis are guaranteed while others are subject to revision according to policy conditions.

Keywords

Medical expenseslifelong health insurance contractmedical inflation indexlapsesurrender valueageing provision
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 47 , Issue 3 , September 2017 , pp. 803 - 836
Copyright
Copyright © Astin Bulletin 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Assuralia (2016) Private ziekteverzekeraars - aantal verzekerde personen. http://www.assuralia.be/fileadmin/content/stats/03_Cijfers_per_tak/05_Gezondheid/04_Aantal_verzekerden/NL/01_Aantal_verzekerden%2001.htm.Google Scholar
Baumann, F., Meier, V. and Werding, M. (2008) Transferable ageing provisions in individual health insurance contracts. German Economic Review, 9 (3), 287–311.Google Scholar
Christiansen, M., Denuit, M. and Dhaene, J. (2014) Reserve–dependent benefits and costs in life and health insurance contracts. Insurance: Mathematics and Economics, 57 (2), 132–137.Google Scholar
Christiansen, M., Eling, M., Schmidt, J.-P. and Zirkelbach, L. (2016) Who is changing health insurance coverage? Empirical evidence on policyholder dynamics. Journal of Risk and Insurance, 83, 269–299.Google Scholar
Cochrane, J. (1995) Time-consistent health insurance. Journal of Political Economy, 103 (3), 445–473.Google Scholar
Denuit, M., Dhaene, J., Hanbali, H., Lucas, N. and Trufin, J. (2017) Updating mechanism for lifelong insurance contracts subject to medical inflation. European Actuarial Journal, 1–31. doi:10.1007/s13385-016-0142-y.Google Scholar
Devolder, P., Denuit, M., Maréchal, X., Yerna, B.-L., Closon, J.-P., Léonard, C., Senn, A. and Vinck, I. (2008) Setting a medical index for private health insurance contracts. KCE reports 96. https://kce.fgov.be/publication/report/setting-a-medical-index-for-private-health-insurance-contracts#.VmLoY7_IYjU.Google Scholar
Dickson, D.C., Hardy, M.R. and Waters, H.R. (2013) Actuarial Mathematics for Life Contingent Risks. Cambridge, UK: Cambridge University Press.Google Scholar
Haberman, S. and Pitacco, E. (1999) Actuarial Models for Disability Insurance. London: CRC Press.Google Scholar
Hofmann, A. and Browne, M. (2013) One-sided commitment in dynamic insurance contracts: Evidence from private health insurance in Germany. Journal of Risk and Uncertainty, 46 (1), 81–112.Google Scholar
Kuo, W., Tsai, C. and Chen, W.-K. (2003) An empirical study on the lapse rate: The cointegration approach. The Journal of Risk and Insurance, 70, 489–508.Google Scholar
Milbrodt, H. (2005) Aktuarielle Methoden der deutschen Privaten Krankenversicherung, Verlag Versicherungswirtsch GmbH, Karlsruhe.Google Scholar
Pauly, M., Kunreuther, H. and Hirth, R. (1995) Guaranteed renewability in insurance. Journal of Risk and Uncertainty, 10 (3), 143–156.Google Scholar
Pitacco, E. (2014) Health Insurance: Basic Actuarial Models. Springer International Publishing.Google Scholar
Vercruysse, W., Dhaene, J., Denuit, M., Pitacco, E. and Antonio, K. (2013) Premium indexing in lifelong health insurance. Far East Journal of Mathematical Sciences, 2013, 365–384.Google Scholar