Innovative Retirement Products
Fall 2020 Actuarial Science and Financial Mathematics Seminar
Date and Time: Wednesday, October 21, 2020, 8:30 AM (CST)
Speaker: An Chen (Institute of Insurance Science, University of Ulm)
Abstract: Tontines and pooled annuities, which are retirement products in which the longevity risk is shared in a pool of policyholders, have recently gained vast attention from researchers and practitioners. These products are cheaper than annuities, but on the other side do not provide stable payments to policyholders. This raises the question whether 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 talk, we analyze and compare three approaches of combining annuities and tontines in an expected utility framework: The tonuity introduced in Chen, Hieber and Klein (2019), a product very similar to the tonuity which we call “antine” and a portfolio consisting of conventional annuities and tontines. Our results show that the novel retirement products antine and tonuity are outperformed by the portfolio. The reason for this is that a policyholder holding a portfolio of annuities and tontines can replicate the payoff of any 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.
In this talk (if time allows), we discuss further conditions under which annuities can be outperformed by tontines. If risk loadings and charges are neglected, a standard expected utility framework, without subjective mortality beliefs, leads to conclude that annuities are always preferred to tontines (Yaari (1965), Milevsky and Salisbury (2015)). In Chen, Hieber and Rach (2020), we show that this result is easily reversed if an individual perceives her peer’s life expectancies to be lower than the ones used by the insurance company.
This talk is based on two papers:
- “Optimal retirement products under subjective mortality beliefs” (2020), with Peter Hieber and Manuel Rach.
- “On the optimal combination of annuities and tontines” (2020), with Manuel Rach and Thorsten Sehner.
Speaker’s Biography: An Chen holds a Ph.D. in Economics from the University of Bonn, and is the chair professor of the Institute of Insurance Science, University of Ulm. She serves as a co-editor of ASTIN Bulletin- the Journal of the International Actuarial Association, and a board member of the German Society for Insurance and Financial Mathematics (DGVFM). Her recent research focuses lie in pension saving product design (to achieve a better risk sharing between insurers and pension beneficiaries), and optimal investment problems, without relying on overly simplifying assumptions about the individual preferences and asset price dynamics. Her works were published in (among others) Journal of Economic Theory, European Journal of Operational Research, Journal of Banking and Finance, ASTIN Bulletin, Insurance: Mathematics and Economics, and Scandinavian Actuarial Journal.