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On the optimal combination of annuities and tontines

Recurso electrónico / Electronic resource
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100  ‎$0‎MAPA20080649999‎$a‎Chen, An
24510‎$a‎On the optimal combination of annuities and tontines‎$c‎An Chen, Manuel Rach, Thorsten Sehner
520  ‎$a‎Tontines, 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.
650 4‎$0‎MAPA20080549206‎$a‎Tontinas
650 4‎$0‎MAPA20080579258‎$a‎Cálculo actuarial
650 4‎$0‎MAPA20080602437‎$a‎Matemática del seguro
650 4‎$0‎MAPA20090039612‎$a‎Planes de jubilación
650 4‎$0‎MAPA20080573614‎$a‎Renta vitalicia
7001 ‎$0‎MAPA20200006633‎$a‎Rach, Manuel
7001 ‎$0‎MAPA20200006640‎$a‎Sehner, Thorsten
7730 ‎$w‎MAP20077000420‎$t‎Astin bulletin‎$d‎Belgium : ASTIN and AFIR Sections of the International Actuarial Association‎$x‎0515-0361‎$g‎01/01/2020 Volumen 50 Número 1 - enero 2020 , p. 95-129