Tonuity: A Novel Individual-Oriented Retirement Plan

Abstract

For insurance companies in Europe, the introduction of Solvency II leads to a tightening of rules for solvency capital provision. In life insurance, this especially affects retirement products that contain a significant portion of longevity risk (e.g., conventional annuities). Insurance companies might react by price increases for those products, and, at the same time, might think of alternatives that shift longevity risk (at least partially) to policyholders. In the extreme case, this leads to so-called tontine products where the insurance company’s role is merely administrative and longevity risk is shared within a pool of policyholders. From the policyholder’s viewpoint, such products are, however, not desirable as they lead to a high uncertainty of retirement income at old ages. In this article, we alternatively suggest a so-called tonuity that combines the appealing features of tontine and conventional annuity. Until some fixed age (the switching time), a tonuity’s payoff is tontine-like, afterwards the policyholder receives a secure payment of a (deferred) annuity. A tonuity is attractive for both the retiree (who benefits from a secure income at old ages) and the insurance company (whose capital requirements are reduced compared to conventional annuities). The tonuity is a possibility to offer tailor-made retirement products: using risk capital charges linked to Solvency II, we show that retirees with very low or very high risk aversion prefer a tontine or conventional annuity, respectively. Retirees with medium risk aversion, however, prefer a tonuity. In a utility-based framework, we therefore determine the optimal tonuity characterized by the critical switching time that maximizes the policyholder’s lifetime utility.

Size-Biased Transform and Conditional Mean Risk Sharing, With Application to P2p Insurance and Tontines

“…Several proposals for mutual inheritance schemes have been made in the literature, including Sabin (2010), Donnelly et al (2014), Donnelly and Young (2017), and Chen et al (2019). As shown by Donnelly (2015), the notion of fairness is very relevant for this kind of mortality pooling scheme.…”

Linking annuity benefits to the longevity experience: alternative solutions

“…We are aware that a traditional theoretical measure expressing the value of the annuity to the individual is the expected utility (which, in the framework of longevity-linked structures, has been considered, e.g. by Valdez et al 2006;Stamos 2008;Donnelly et al 2013;Maurer et al 2013;Milevsky & Salisbury 2015;Bravo & de Freitas 2018;Chen et al 2019). We do not perform an assessment in this respect because we prefer to address quantities which are easier to understand by the individual.…”

“…Originally developed for speculative purposes, tontine annuities have recently been revised as a form of longevity risk management. See, for example, McKeever (2009), Baker & Siegelman (2010), Sabin (2010), Milevsky (2014), Milevsky & Salisbury (2015), Milevsky & Salisbury (2016), Weinert & Gründl (2016), and Chen et al (2019).…”

Optimal portfolio choice with tontines under systematic longevity risk

“…McKeever (2009), Milevsky (2015), and Li & Rothschild (2019) review the historical development of tontines. Sabin (2010), Milevsky & Salisbury (2015), and Milevsky & Salisbury (2016) study actuarially fair and optimal payout structures of tontines, and Chen et al (2019) analyse the effects of combining a tontine and an annuity into a unified product. Weinert (2017a) estimates the cost of a tontine compared to traditional life insurance products from an economic as well as a regulatory perspective.…”