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ON THE OPTIMAL COMBINATION OF ANNUITIES AND TONTINES

Published online by Cambridge University Press:  31 January 2020

An Chen ,
Manuel Rach  and
Thorsten Sehner Open the ORCID record for Thorsten Sehner [Opens in a new window]
An Chen
Affiliation:
Institute of Insurance Science Ulm UniversityHelmholtzstraβe 20 89069 Ulm, Germany E-Mail: an.chen@uni-ulm.de
Manuel Rach*
Affiliation:
Institute of Insurance Science Ulm UniversityHelmholtzstraβe 20 89069 Ulm, Germany E-Mail: manuel.rach@uni-ulm.de
Thorsten Sehner
Affiliation:
Institute of Insurance Science Ulm UniversityHelmholtzstraβe 20 89069 Ulm, Germany E-Mail: thorsten.sehner@uni-ulm.de
*
E-Mail: manuel.rach@uni-ulm.de
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Abstract

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Tontines, retirement products constructed in such a way that the longevity risk is shared in a pool of policyholders, have recently gained vast attention from researchers and practitioners. Typically, these products are cheaper than annuities, but do not provide stable payments to policyholders. This raises the question whether, from the policyholders' viewpoint, the advantages of annuities and tontines can be combined to form a retirement plan which is cheaper than an annuity, but provides a less volatile retirement income than a tontine. In this article, we analyze and compare three approaches of combining annuities and tontines in an expected utility framework: the previously introduced “tonuity”, a product very similar to the tonuity which we call “antine” and a portfolio consisting of an annuity and a tontine. We show that the payoffs of a tonuity and an antine can be replicated by a portfolio consisting of an annuity and a tontine. Consequently, policyholders achieve higher expected utility levels when choosing the portfolio over the novel retirement products tonuity and antine. Further, we derive conditions on the premium loadings of annuities and tontines indicating when the optimal portfolio is investing a positive amount in both annuity and tontine, and when the optimal portfolio turns out to be a pure annuity or a pure tontine.

Keywords

Optimal retirement productsannuitytontinetonuityantineG22J32

Information

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 50 , Issue 1 , January 2020 , pp. 95 - 129
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
© Astin Bulletin 2020

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