# Modern tontine with bequest: innovation in pooled annuity products

## TL;DR

This paper proposes a novel pension product combining a tontine mechanism with a bequest feature, analyzing optimal allocation strategies for retirees with varying risk preferences under a new pooled annuity structure.

## Contribution

It introduces a new pooled annuity product with a dynamic re-balancing feature and analyzes optimal pension savings allocation based on risk aversion levels.

## Key findings

- More risk-averse retirees allocate a stable proportion to the tontine.
- Less risk-averse retirees' allocation decreases temporarily but increases at very old ages.
- Least risk-averse retirees may allocate a high proportion to the tontine for potential bequest benefits.

## Abstract

We introduce a new pension product that offers retirees the opportunity for a lifelong income and a bequest for their estate. Based on a tontine mechanism, the product divides pension savings between a tontine account and a bequest account. The tontine account is given up to a tontine pool upon death while the bequest account value is paid to the retiree's estate. The values of these two accounts are continuously re-balanced to the same proportion, which is the key feature of our new product. Our main research question about the new product is what proportion of pension savings should a retiree allocate to the tontine account. Under a power utility function, we show that more risk averse retirees allocate a fairly stable proportion of their pension savings to the tontine account, regardless of the strength of their bequest motive. The proportion declines as the retiree becomes less risk averse for a while. However, for the least risk averse retirees, a high proportion of their pension savings is optimally allocated to the tontine account. This surprising result is explained by the least risk averse retirees seeking the potentially high value of the bequest account at very old ages.