Optimal hurdle rate and investment policy in lifetime pension pools

Lifetime pension pools—also known as group self-annuitization plans, pooled annuity funds, and variable payment life annuities in the literature—offer retirees lifelong income by collectively managing mortality risk and adjusting benefits based on the investment performance and the mortality experience within the pool. The benefit structure hinges on two key design parameters: the investment policy and the hurdle rate. However, past research offers limited guidance on optimal asset allocation in such settings, often relying on overly simplistic strategies. Furthermore, the choice of hurdle rate has received virtually no attention in the literature. This study addresses this gap by jointly analyzing optimal hurdle rates and investment strategies using a dynamic programming approach that allows for varying degrees of risk aversion via a hyperbolic absolute risk aversion utility function. Our findings reveal that, as risk aversion increases, the model favours more conservative portfolios and lower hurdle rates; conversely, lower risk aversion supports riskier allocations and higher hurdle rates. The threshold parameter—which reflects the minimum acceptable level of consumption—plays a critical role in shaping the hurdle rate behaviour.