Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, October 21, 2020.

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events for the
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Questions regarding events or the calendar should be directed to Tori Corkery.
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Wednesday, October 21, 2020

8:30 am in via Zoom (contact wfchong@illinois.edu) for link,Wednesday, October 21, 2020

#### Innovative Retirement Products

###### 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.