On the Optimal Combination of Annuities and Tontines
By An Chen, Manuel Rach, Thorsten Sehner
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.
Source: SSRN
