Working longer, not harder: Target wealth, leisure, and retirement

We study a continuous-time life-cycle problem in which an agent chooses consumption, portfolio allocation, leisure, and an endogenous retirement time subject to a target-wealth requirement. The agent trades in a complete market with labor income and has Cobb-Douglas preferences over consumption and leisure. Using a dual martingale approach, we provide closed-form solutions for the optimal policies and wealth boundaries. We show that the impact of the wealth target on consumption and risk-taking depends on the preference weight on consumption: a higher target leads to higher pre-retirement consumption and conservative investment when the consumption weight is low, but this pattern reverses when the weight is high. Crucially, tighter targets are accommodated primarily through the extensive margin: the expected retirement time increases significantly, while the pre-retirement leisure intensity remains largely insensitive. Our results thus imply that target-wealth requirements are met by working longer, not harder.