Unemployment Risks and Optimal Retirement in an Incomplete Market
研究个体面临不可对冲的失业风险时，如何同时决定最优消费、投资和退休时间，模型解释了低消费、风险投资行为以及穷人持有更多股票的现象。
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 an 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 for relatively higher stock holdings of the poor. We also analyze the sensitivity of an individual’s optimal behavior in changing her wealth level, investment opportunity, and the magnitude of preference for postretirement leisure. Finally, we find that our model explains a countercyclical pattern of the number of unemployed job leavers.