Controlling investment risk in a pooled annuity fund to improve income withdrawals

Pooled annuity fund offer a third way of decumulation, between life annuities and income drawdown (called programmed withdrawals). In such funds, participants receive an income while they are alive. Their account values within the fund earn both investment returns and an additional return due to the pooling of longevity risk.A question of how to invest in such funds is studied here. In the absence of systematic longevity risk and no re-investment risk, a guaranteed minimum income can be secured by investing entirely in the risk-free asset. How should a participant invest if they wish to have a higher income?An optimal strategy is derived, based on a quadratic loss function. The strategy shows increasing risk aversion with time, as well as responding to gains and losses above a target value. Analysis of numerical simulations shows that the desired income to be withdrawn must be chosen carefully, so as to enable investment risk-taking and hence the income to be achieved with a reasonable chance.