Optimal Retirement with Borrowing Constraints and Forced Unemployment Risk

In this paper, we develop a new dynamic programming approach for solving an optimal retirement model in a two-dimensional incomplete market, which is induced by forced unemployment risk and borrowing constraints. We show that the two dimensions jointly affect an individual's optimal consumption, investment, and retirement strategies. Specifically, we find that there exists a certain endogenously determined wealth threshold over which it is optimal for an individual to enter retirement. Comparing to standard literature, the wealth threshold is lower in the presence of the two-dimensional market incompleteness, implying an earlier retirement than would be suggested by a complete market model. As a result, neglecting the two-dimensional market incompleteness can be costly to an individual who aims to attain her goal of optimal retirement