Optimal annuitization and asset allocation with fixed transaction costs

In this paper, we examine optimal annuitization and asset allocation strategies for a utility-maximizing retiree with constant absolute risk aversion (CARA). The retiree can invest in a market consisting of one risky asset and one risk-free asset and is also allowed to purchase life annuities, with each purchase of life annuities incurring a fixed transaction cost. By using a stochastic control approach and duality techniques, we find that the optimal annuitization strategy is a barrier strategy involving a lower and an upper barrier on the retiree’s wealth. Once the wealth reaches the upper barrier, the retiree purchases additional annuity income to reduce the wealth to the lower one. Furthermore, we provide several numerical examples to illustrate our results and analyze the sensitivity of various parameters. We also compare these optimal strategies with those in the constrained Merton model and the scenario without transaction costs. Numerical results indicate that transaction costs cannot only postpone the retiree’s decision on annuitizing additional wealth, but also result in underspending and slow drawdown rate in the decumulation phases, which provides further explanations for the annuity puzzle, retirement-consumption puzzle and retirement-savings puzzle. Finally, we conduct perturbation analysis and find an asymptotic approximation of the value function when the transaction fee is small.