Unemployment Risks and Optimal Retirement in an Incomplete Market

We develop a new approach for solving the optimal retirement problem for an individual with an unhedgeable income risk. The income risk stems from a forced unemployment event, which occurs as an exponentially-distributed random shock. The optimal retirement problem is to determine the individual's optimal consumption and investment behaviors and optimal retirement time simultaneously. We introduce a new convex-duality approach for reformulating the original retirement problem and provide an iterative numerical method to solve it. Reasonably calibrated parameters say that our model can give an explanation for lower consumption and risky investment behaviors of individuals and a relatively higher stock holdings for the poor. We also analyze the sensitivity of an individual's optimal behaviors in changing her wealth level, investment opportunity, and the magnitude of preference for post-retirement leisure. Finally, we find our model explains a procyclical pattern of the number of unemployed job leavers