ON THE OPTIMAL COMBINATION OF ANNUITIES AND TONTINES

An Chen, Manuel Rach and Thorsten Sehner

ASTIN Bulletin, 2020, vol. 50, issue 1, 95-129

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.

Date: 2020
References: Add references at CitEc
Citations: View citations in EconPapers (9)

Downloads: (external link)
https://www.cambridge.org/core/product/identifier/ ... type/journal_article link to article abstract page (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cup:astinb:v:50:y:2020:i:1:p:95-129_4

Access Statistics for this article

More articles in ASTIN Bulletin from Cambridge University Press Cambridge University Press, UPH, Shaftesbury Road, Cambridge CB2 8BS UK.
Bibliographic data for series maintained by Kirk Stebbing ().