Tontines, and the law of large numbers

Tontines, and the law of large numbers

Added in LIFE PENSIONS 2019 JUL | IME 2019

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Combining the best of drawdown and annuity, the investment returns and the longevity credits, tontines offer a great alternative to current pension products. Tontines are well-understood under the assumption of constant market returns and a perfect pool. However the literature lacks in understanding of the impact of fluctuating market returns and realized mortality rates. We present a numerical study that analyzes how many members a tontine need in order to deliver the outcome that idealized results suggest. We assume a heterogeneous member profile, an explicit tontine scheme, and a Black-Scholes market. We give a practical answer that shall be used in the future for pension products in the UK market. In the end, we compare our result with the 1000-member rule by Qiao and Sherris for Group-Self-Annuitization-Schemes from 2013.

[1] Qiao, C. and Sherris, M. (2013), “Managing Systematic Mortality Risk with Group Self-Pooling and Annuitization Schemes.” Journal of Risk and Insurance, vol. 80(4), pp. 949_974.

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