This paper studies the portfolio management problem for an individual with a non-exponential discount function and habit formation in finite time. The investor receives a deterministic income, invests in risky assets, buys insurance and consumes continuously. The objective is to maximize the utility of excessive consumption, heritage and terminal wealth. The non-exponential discounting makes the optimal strategy adopted by a naive person time-inconsistent. The equilibrium for a sophisticated person is Nash subgame perfect equilibrium, and the sophisticated person is time-consistent. We calculate the analytical solution for both the naive strategy and equilibrium strategy in the CRRA case and compare the results of the two strategies. By numerical simulation, we find that the sophisticated individual will spend less on consumption and insurance and save more than the naive person. The difference in the strategies of the naive and sophisticated person decreases over time. Furthermore, if an individual of either type is more patient in the future or has a greater tendency toward habit formation, he/she will consume less and buy less insurance, and the degree of inconsistency will also be increased. The sophisticated person's consumption and habit level are initially lower than those of a naive person but are higher in later periods.

中文翻译：

---

具有习惯养成的非指数折现投资组合管理

本文研究了具有非指数折现功能和在有限时间内养成习惯的个人的投资组合管理问题。投资者获得确定的收入，投资于风险资产，购买保险并持续消费。目的是最大程度地利用过度消费，遗产和终端财富。非指数折扣使天真人采用的最优策略在时间上不一致。一个老练的人的均衡是纳什子博弈的完美均衡，老练的人是时间一致的。我们为CRRA案例计算了幼稚策略和均衡策略的解析解，并比较了这两种策略的结果。通过数值模拟 我们发现，与天真的人相比，有经验的人将在消费和保险上花费更少，而储蓄更多。天真的和老练的人在策略上的差异随着时间的推移而减小。此外，如果任何一种类型的人将来都有更多的耐心或更容易养成习惯，那么他/她将减少消费并购买较少的保险，不一致的程度也会增加。有经验的人的消费和习惯水平最初低于天真的人，但在后期则更高。他/她将减少消费，减少购买保险，不一致的程度也会增加。有经验的人的消费和习惯水平最初低于天真的人，但在后期则更高。他/她将减少消费，减少购买保险，不一致的程度也会增加。有经验的人的消费和习惯水平最初低于天真的人，但在后期则更高。