Determining the retirement time using dynamic programming

Specialeforsvar ved Frederik Dyhl Østerkryger

Titel: Determining the retirement time using dynamic programming

Abstract: The choice of retirement age is increasingly important in Denmark with increasing longevity and eligible age for state pension. This thesis studies the problem of a suitable retirement time for a finitely lived agent having a Cobb-Douglas utility function with consumption and leisure as the commodities. Using optimal control theory, in the form of HJB-equations, we show that truncating a fixed leisure function or mixing leisure with the value function at time t = 0 are both viable methods in order to obtain analytical solutions. Here, we see that the latter method adds the possibility of early retirement through the leisure function. Finally, we study a numerical example investigating the impact mortality and a stochastic market have on the time of retirement, and how chang-ing the individual preference parameters, i.e., risk aversion, consumption preferences and impatience change the outcome. We find that mortality had the biggest impact for an old agent, where the stochastic market made the biggest decrease in the time of retirement for a young agent. However, the agent with fixed leisure did not care about investment opportunities, revealing realistic retirement times are obtained for different preference parameters for old and young agents using this method. Finally, in the full model, variations in risk aversion, consumption preferences and impatience had monotone impacts on the retirement ages (and welfare-loss for the agent mixing the value function and leisure) in all cases.

Vejleder: Mogens Steffensen
Censor:   Kenneth Bruhn, Edlund