Time-inconsistent life-cycle consumption and retirement choice with mortality risk

Abstract

In this paper, we propose a general model to study life-cycle consumption and retirement choice of individuals with mortality risk and various forms of discounting preference. By solving the Euler-Lagrange equations, we obtain the optimal consumption strategy explicitly and provide an equation to solve for optimal retirement age. Two intuitive budget constraints are established to demonstrate the effects of precautionary saving and bequest motives on the optimal choices. We also explore the effects of interest rate, income and discounting preference on the optimization, where numerical examples are used to illustrate the role of these factors on the consumption behavior and retirement timing.