An Integral Equation Representation for Optimal Retirement Strategies in Portfolio Selection Problem

In this paper we study the consumption and portfolio selection problem of a finitely-lived economic agent with an early retirement option, that is, the agent can choose her/his early retirement time before a mandatory retirement time. Based on the theoretical results in Yang and Koo (Math Oper Res, 43(4):1378–1404, 2018), we derive an integral equation satisfied by the optimal retirement boundary or free boundary using the Mellin transform technique. We also derive integral equation representations for the optimal consumption-portfolio strategies and the optimal wealth process. By using the recursive integration method, we obtain the numerical solutions for the integral equations and discuss economic implications for the optimal retirement strategies by using numerical solutions.