Consumption-portfolio choice with subsistence consumption and risk aversion change at retirement

Abstract

Abstract This paper considers subsistence consumption of an economic agent both before and after retirement in analyzing the optimal consumption, portfolio, and retirement problem. We allow the relative risk aversion of the economic agent to make a one-off jump at retirement. With a Cobb–Douglas utility function, we obtain explicit expressions for the optimal policies. Numerical results show that, whereas post-retirement subsistence consumption tends to delay retirement, pre-retirement subsistence consumption and the magnitude of jump in relative risk aversion may stimulate early retirement. Also, the consumption drop at retirement deepens as post-retirement subsistence consumption increases, but it weakens as pre-retirement subsistence consumption increases.

Keywords

• Dynamic programming method
• Free boundary value problem
• Optimal stopping time
• Risk aversion change
• Subsistence consumption