Retirement with Perfect Insurance

This paper focuses on the relation between worker's productivity and retirement decision. Assuming that productivity follows geometric Brownian motion with drift, there exists such a level of productivity for which it is optimal to retire. The worker buys an insurance, which gives a constant income and retirement benefits in exchange for the total output. The level of income and benefits is set to maximize lifetime utility. In such framework we find the retirement threshold of productivity and the probability of retirement.