DISUTILITY, OPTIMAL RETIREMENT, AND PORTFOLIO SELECTION

Kyoung Jin Choi and Gyoocheol Shim

Mathematical Finance, 2006, vol. 16, issue 2, 443-467

Abstract: We study the optimal retirement and consumption/investment choice of an infinitely‐lived economic agent with a time‐separable von Neumann–Morgenstern utility. A particular aspect of our problem is that the agent has a retirement option. Before retirement the agent receives labor income but suffers a utility loss from labor. By retiring, he avoids the utility loss but gives up labor income. We show that the agent retires optimally if his wealth exceeds a certain critical level. We also show that the agent consumes less and invests more in risky assets when he has an option to retire than he would in the absence of such an option. An explicit solution can be provided by solving a free boundary value problem. In particular, the critical wealth level and the optimal consumption and portfolio policy are provided in explicit forms.

Date: 2006
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