Recently, [7, Journal of Economic Dynamics and Control] studied the optimal consumption and investment problem in the early retirement model of [6, Journal of Financial Economics], incorporating a target wealth constraint at the time of retirement. Specifically, they required that the agent’s wealth at the time of early retirement be greater than or equal to a predetermined level. To obtain their results, several assumptions were imposed on the market parameters. In this paper, we extend their results to a general utility function, without imposing specific conditions on the parameters. From a mathematical perspective, the obstacle problem that arises in this context is particularly challenging due to the lack of monotonicity in the obstacle. Nevertheless, we overcome this difficulty through rigorous analysis. We illustrate the applicability of our results through numerical examples under HARA and CARA utility specifications.
