We study the consumption and portfolio decisions by incorporating mortality risk and altruistic factor in the classical model of Merton (Rev Econ Stat 51:247–257, 1969; J Econ Theory 3:373–413, 1971) and Yaari (Rev Econ Stud 32(2):137–150, 1965). We find that besides the present-biased preference, the process of updating mortality information may be another underlying cause of dynamically time-inconsistent consumption behavior. We use the game-theoretic approach to obtain the extended Hamilton–Jacobi–Bellman equation. Furthermore, we obtain the closed-form solution for the logarithmic utility and explore comparative statics and implications for dynamic behavior. We present numerical results for the power utility that shows the sophisticated individual enjoys higher expected discounted utility than the naive. Our analytical solution enables us to generate a set of testable predictions that are consistent with existing empirical evidence. In particular, we show that for a moderate range of expected investment return, individuals will exhibit a “hump-shaped” consumption pattern, as widely documented in the empirical literature.

中文翻译：

---

寿命不确定的消费和投资组合决策

我们通过将死亡风险和利他因素纳入默顿经典模型（Rev Econ Stat 51：247–257，1969； J Econ Theory 3：373–413，1971）和Yaari（Rev Econ Stud 32）中来研究消费和投资组合决策。 （2）：137-150，1965年）。我们发现，除了当前偏向的偏好之外，更新死亡率信息的过程可能是动态时间不一致的消费行为的另一个潜在原因。我们使用博弈论方法来获得扩展的汉密尔顿-雅各比-贝尔曼方程。此外，我们获得了对数效用的闭式解，并探索了比较静力学及其对动态行为的影响。我们提供的电力效用的数值结果表明，成熟的个人比天真的人享有更高的期望折扣效用。我们的分析解决方案使我们能够生成与现有经验证据一致的一组可检验的预测。特别是，我们证明，在适度的预期投资回报范围内，个人将表现出“驼峰形”的消费模式，这在经验文献中得到了广泛的证明。