On the Optimal Combination of Annuities and Tontines

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.

A Proposal of a Pension Plan Design Based on Collective Pension Funds

“…The most recent ones are by Chen et al (2020) mention that these products can be combined to form a retirement plan that is cheaper than an annuity but provides a less volatile retirement income than a tontine. However, it is also mentioned that subjective mortality beliefs influence the optimal choice between annuities and tontines, with tontines being preferred by those who underestimate average life expectancy.…”

On the Unfairness of Actuarial Fair Annuities

“…Note that this definition of expected lifetime utility is based on the independence assumption between mortality and financial market risk. This approach is fairly standard in the literature on retirement products; see, e.g., Yaari (1965) and Chen et al (2020).…”

Designing Annuities with Flexibility Opportunities in an Uncertain Mortality Scenario

“…Several opportunities for innovation can be obtained when combining different benefits, such as the just mentioned case of annuities and death benefits. Particularly interesting in this regard is the combination of different forms of annuities; Chen et al ( , 2020 and Chen and Rach (2019) consider the case of fixed annuity benefits combined with mortality/longevity linked-benefits.…”