We study a discrete-time life cycle retirement planning problem for individual workers with four distinct investment options: self-management with dynamic investment (S), self-management with benchmark investment (B), hire-management with flexible allocation ($\text{H}_{1}$), and hire-management with alpha focus ($\text{H}_{2}$). We examine the investment strategies and consumption patterns during the defined contribution fund accumulation period, ending with a life annuity purchase at retirement to finance post-retirement consumption. Based on the calibrated model using US data, we employ numerical dynamic programming technique to optimize worker’s financial decisions. Our analysis reveals that, despite the agency risk, delegated investments can add value to a worker’s lifetime utility, with the $\text{H}_2$ option yielding the best lifetime utility outcome. However, after taking the fund management fee into consideration, we find that both the $\text{H}_1$ and $\text{H}_2$ options may not offer additional value compared to the S option, yet they still surpass the B option in performance.

An abstract gambler's problem is formulated in a continuous-time setting and analogues are proved for some of the discrete-time results of Dubins and Savage in their book How to Gamble if You Must. Applications are made to problems of controlling a Brownian motion process.