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SOLVENCY REQUIREMENT IN A UNISEX MORTALITY MODEL

Published online by Cambridge University Press:  25 April 2018

An Chen ,
Montserrat Guillen  and
Elena Vigna
An Chen
Affiliation:
Faculty of Mathematics and Economics, University of Ulm, Helmholtzstrasse 20, 89069 Ulm, Germany E-Mail: an.chen@uni-ulm.de
Montserrat Guillen
Affiliation:
Department of Econometrics, University of Barcelona, Riskcenter-IREA, Av. Diagonal 690, 08034 Barcelona, Spain E-mail: mguillen@ub.edu
Elena Vigna*
Affiliation:
University of Torino, Collegio Carlo Alberto and CeRP, Corso Unione Sovietica 218 bis, 10134 Torino, Italy
*
E-Mail: elena.vigna@unito.it
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Abstract

Following the EU Gender Directive, that obliges insurance companies to charge the same premium to policyholders of different genders, we address the issue of calculating solvency capital requirements (SCRs) for pure endowments and annuities issued to mixed portfolios. The main theoretical result is that, if the unisex fairness principle is adopted for the unisex premium, the SCR at issuing time of the mixed portfolio calculated with unisex survival probabilities is greater than the sum of the SCRs of the gender-based subportfolios. Numerical results show that for pure endowments the gap between the two is negligible, but for lifetime annuities the gap can be as high as 3–4%. We also analyze some conservative pricing procedures that deviate from the unisex fairness principle, and find that they lead to SCRs that are lower than the sum of the gender-based SCRs because the policyholders are overcharged at issuing time.

Keywords

SCRlife insurance pricingunisex tariffunisex fairness principlelife tablerisk marginGender Directivegender discriminationC1C13C18C38J11
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 48 , Issue 3 , September 2018 , pp. 1219 - 1243
Copyright
Copyright © Astin Bulletin 2018 

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References

Aseervatham, V., Lex, C. and Spindler, M. (2016) How do unisex rating regulations affect gender differences in insurance premiums? The Geneva Papers on Risk and Insurance Issues and Practice, 41 (1), 128–160.Google Scholar
Biffis, E. (2005) Affine processes for dynamic mortality and actuarial valuations. Insurance: Mathematics and Economics, 37 (3), 443–468.Google Scholar
Börger, M. (2010) Deterministic shock vs. stochastic value-at-risk, an analysis of the solvency II standard model approach to longevity risk. Blätter der DGVFM, 31 (2), 225–259.Google Scholar
Chen, A. and Vigna, E. (2017) A unisex stochastic mortality model to comply with EU Gender Directive. Insurance: Mathematics and Economics, 73, 124–136.Google Scholar
Dahl, M. (2004) Stochastic mortality in life insurance: Market reserves and mortality-linked insurance contracts. Insurance: Mathematics and Economics, 35 (1), 113–136.Google Scholar
Duffie, D., Pan, J. and Singleton, K. (2000) Transform analysis and asset pricing for affine jump-diffusions. Econometrica, 68 (6), 1343–1376.Google Scholar
EIOPA (2014). Technical specifications for the Solvency II Preparatory Phase - Part I. Technical report, European Insurance and Occupational Pensions Authority.Google Scholar
Guillen, M. (2012) Sexless and beautiful data: From quantity to quality. Annals of Actuarial Science, 6 (02), 231–234.Google Scholar
Lin, Y. and Cox, S. H. (2005) Securitization of mortality risks in life annuities. Journal of Risk and Insurance, 72 (2), 227–252.Google Scholar
Luciano, E. and Vigna, E. (2008) Mortality risk via affine stochastic intensities: Calibration and empirical relevance. Belgian Actuarial Bulletin, 8 (1), 5–16.Google Scholar
Milevsky, M. A. and Promislow, S. D. (2001) Mortality derivatives and the option to annuitise. Insurance: Mathematics and Economics, 29 (3), 299–318.Google Scholar
Milevsky, M. A. and Salisbury, T. S. (2015) Optimal retirement income tontines. Insurance: Mathematics and Economics, 64, 91–105.Google Scholar
Olivieri, A. and Pitacco, E. (2009) Stochastic mortality: The impact on target capital. ASTIN Bulletin, 39 (02), 541–563.Google Scholar
Ornelas, A. and Guillen, M. (2013) A comparison between general population mortality and life tables for insurance in Mexico under gender proportion inequality. Revista de Métodos Cuantitativos para la Economía y la Empresa. Journal of Quantitative Methods for Economics and Business Administration, 16 (1), 47–67.Google Scholar
Sass, J. and Seifried, F. T. (2014) Insurance markets and unisex tariffs: Is the European Court of Justice improving or destroying welfare? Scandinavian Actuarial Journal, 2014 (3), 228–254.Google Scholar
Schmeiser, H., Störmer, T. and Wagner, J. (2014) Unisex insurance pricing: Consumers' perception and market implications. The Geneva Papers on Risk and Insurance Issues and Practice, 39 (2), 322–350.Google Scholar
Thiery, Y. and Van Schoubroeck, C. (2006) Fairness and equality in insurance classification. The Geneva Papers on Risk and Insurance Issues and Practice, 31 (2), 190–211.Google Scholar
University of California, Berkeley (USA) and Max Planck Institute for Demographic Research (Germany) (2002) Human Mortality Database. Available at www.mortality.org or www.humanmortality.de.Google Scholar