Combining Annuities and Tontines

On the Optimal Combination of Annuities and Tontines

33 Pages Posted: 5 Aug 2019

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: August 1, 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 and carries less risk than a tontine. In this article, we analyze and compare three approaches of combining annuities and tontines in an expected utility framework: The “tonuity” introduced in Chen et al. (2019), 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 or 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.

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 (August 1, 2019). Available at SSRN: https://ssrn.com/abstract=3430546 or http://dx.doi.org/10.2139/ssrn.3430546