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TONUITY: A NOVEL INDIVIDUAL-ORIENTED RETIREMENT PLAN

Published online by Cambridge University Press:  26 December 2018

An Chen ,
Peter Hieber  and
Jakob K. Klein
An Chen
Affiliation:
Institute of Insurance ScienceUniversity of Ulm, Ulm, Germany E-Mail: an.chen@uni-ulm.de
Peter Hieber
Affiliation:
Institute of Insurance ScienceUniversity of Ulm, Ulm, Germany E-Mail: peter.hieber@uni-ulm.de
Jakob K. Klein*
Affiliation:
Institute of Insurance ScienceUniversity of Ulm, Ulm, Germany E-Mail: jakob.klein@uni-ulm.de
*
E-Mail: jakob.klein@uni-ulm.de
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Abstract

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For insurance companies in Europe, the introduction of Solvency II leads to a tightening of rules for solvency capital provision. In life insurance, this especially affects retirement products that contain a significant portion of longevity risk (e.g., conventional annuities). Insurance companies might react by price increases for those products, and, at the same time, might think of alternatives that shift longevity risk (at least partially) to policyholders. In the extreme case, this leads to so-called tontine products where the insurance company’s role is merely administrative and longevity risk is shared within a pool of policyholders. From the policyholder’s viewpoint, such products are, however, not desirable as they lead to a high uncertainty of retirement income at old ages. In this article, we alternatively suggest a so-called tonuity that combines the appealing features of tontine and conventional annuity. Until some fixed age (the switching time), a tonuity’s payoff is tontine-like, afterwards the policyholder receives a secure payment of a (deferred) annuity. A tonuity is attractive for both the retiree (who benefits from a secure income at old ages) and the insurance company (whose capital requirements are reduced compared to conventional annuities). The tonuity is a possibility to offer tailor-made retirement products: using risk capital charges linked to Solvency II, we show that retirees with very low or very high risk aversion prefer a tontine or conventional annuity, respectively. Retirees with medium risk aversion, however, prefer a tonuity. In a utility-based framework, we therefore determine the optimal tonuity characterized by the critical switching time that maximizes the policyholder’s lifetime utility.

Keywords

Longevity risktontinesSolvency IIpooled annuitiescapital requirementslifetime utility
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 49 , Issue 1 , January 2019 , pp. 5 - 30
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
Copyright © Astin Bulletin 2018

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