  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.
