On the Optimal Combination of Annuities and Tontines

41 Pages Posted: 5 Aug 2019 Last revised: 2 Dec 2019

See all articles by An Chen

An Chen

University of Ulm

Manuel Rach

University of Ulm - Institute of Insurance Science

Thorsten Sehner

University of Ulm - Department of Mathematics and Economics

Date Written: November 29, 2019

Abstract

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 products, annuity, tontine, tonuity, antine

JEL Classification: G22, J32

Suggested Citation

Chen, An and Rach, Manuel and Sehner, Thorsten, On the Optimal Combination of Annuities and Tontines (November 29, 2019). Available at SSRN: https://ssrn.com/abstract=3430546 or http://dx.doi.org/10.2139/ssrn.3430546

An Chen

University of Ulm ( email )

Helmholtzstrasse 20
Ulm, D-89081
Germany

HOME PAGE: http://www.uni-ulm.de/mawi/ivw/team

Manuel Rach (Contact Author)

University of Ulm - Institute of Insurance Science ( email )

Ulm, 89081
Germany

Thorsten Sehner

University of Ulm - Department of Mathematics and Economics ( email )

20, Helmholzstrasse
Ulm, DE 89069
Germany
(+49)731/50-30915 (Phone)
(+49)731/50-31188 (Fax)

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