A dynamic programming approach to a consumption/investment and retirement choice problem under borrowing constraints

Abstract

In this paper we consider an optimization problem of an infinitely lived working agent with an option to retire who maximizes the utility from her lifetime consumption. The agent receives labor income during the period before her voluntary retirement, but suffers disutility from labor. Moreover, the agent lacks the means to borrow against her future labor income. We use the dynamic programming approach to derive the closed-form solutions and provide some numerical illustrations.