<p style='text-indent:20px;'>This paper studies the optimal consumption, life insurance and investment problem for an income earner with uncertain lifetime under smooth ambiguity model. We assume that risky assets have unknown market prices that result in ambiguity. The individual forms his belief, that is, the distribution of market prices, according to available information. His ambiguity attitude, which is similar to the risk attitude described by utility function <inline-formula><tex-math id="M1">\begin{document}$ U $\end{document}</tex-math></inline-formula>, is represented by an ambiguity preference function <inline-formula><tex-math id="M2">\begin{document}$ \phi $\end{document}</tex-math></inline-formula>. Under the smooth ambiguity model, the problem becomes time-inconsistent. We derive the extended Hamilton-Jacobi-Bellman (HJB) equation for the equilibrium value function and equilibrium strategy. Then, we obtain the explicit solution for the equilibrium strategy when both <inline-formula><tex-math id="M3">\begin{document}$ U $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$ \phi $\end{document}</tex-math></inline-formula> are power functions. We find that a more risk- or ambiguity-averse individual will consume less, buy more life insurance and invest less. Moreover, we find that the Tobin-Markowitz separation theorem is no longer applicable when ambiguity attitude is taken into consideration. The investment strategy will change with the characteristics of the decision maker, such as risk attitude, ambiguity attitude and age.</p>

中文翻译：

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平滑模糊下的时间一致的生命周期投资组合选择

<p style='text-indent:20px;'>本文研究了在平滑模糊模型下，不确定寿命的收入者的最优消费、人寿保险和投资问题。我们假设风险资产具有未知的市场价格，从而导致模糊性。个人根据现有信息形成他的信念，即市场价格的分布。他的模棱两可态度，类似于效用函数描述的风险态度 <inline-formula><tex-math id="M1">\begin{document}$ U $\end{document}</tex-math>< /inline-formula>，由歧义偏好函数表示 <inline-formula><tex-math id="M2">\begin{document}$ \phi $\end{document}</tex-math></内联公式>。在平滑模糊模型下，问题变得时间不一致。我们推导出平衡价值函数和平衡策略的扩展 Hamilton-Jacobi-Bellman (HJB) 方程。然后，当 <inline-formula><tex-math id="M3">\begin{document}$ U $\end{document}</tex-math></inline -formula> 和 <inline-formula><tex-math id="M4">\begin{document}$ \phi $\end{document}</tex-math></inline-formula> 是幂函数。我们发现，一个更厌恶风险或模棱两可的人会减少消费，购买更多人寿保险并减少投资。此外，我们发现当考虑歧义态度时，托宾-马科维茨分离定理不再适用。