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.

在本文中，我们提出了一个通用模型来研究具有死亡风险和各种形式的贴现偏好的个体的生命周期消费和退休选择。通过求解欧拉-拉格朗日方程，我们明确地得到了最优消费策略，并提供了求解最优退休年龄的方程。建立了两个直观的预算约束来证明预防性储蓄和遗赠动机对最优选择的影响。我们还探讨了利率、收入和贴现偏好对优化的影响，并通过数值例子来说明这些因素对消费行为和退休时间的作用。