标题： 健康冲击风险下具有消费习惯的家庭最优投资、消费和人寿保险决策 显示英文标题

标题： Optimal investment, consumption and life insurance decisions for households with consumption habits under the health shock risk

摘要： 本文研究了健康冲击风险影响下家庭最优投资、消费和人寿保险策略。考虑到家庭成员未来健康状况的不确定性，采用非齐次马尔可夫过程建模养家人的健康状态。基于习惯形成理论，探讨了不同的消费习惯对家庭投资、消费和人寿保险策略的影响。根据养家人是否健在，分别建立并求解了养家人存活和去世两种情况下的Hamilton-Jacobi-Bellman (HJB)方程，得到了最优投资、消费和人寿保险策略的显式表达式。通过灵敏度分析表明，家庭内部存在健康冲击会对投资和消费决策产生负面影响，而消费习惯的形成会增加家庭的预防性储蓄倾向。 显示英文摘要

摘要： This paper investigates the optimal investment, consumption, and life insurance strategies for households under the impact of health shock risk. Considering the uncertainty of the future health status of family members, a non-homogeneous Markov process is used to model the health status of the breadwinner. Drawing upon the theory of habit formation, we investigate the influence of different consumption habits on households' investment, consumption, and life insurance strategies. Based on whether the breadwinner is alive or not, we formulate and solve the corresponding Hamilton-Jacobi-Bellman (HJB) equations for the two scenarios of breadwinner survival and breadwinner's demise, respectively, and obtain explicit expressions for the optimal investment, consumption, and life insurance strategies. Through sensitivity analysis, it has been shown that the presence of health shocks within households has a negative impact on investment and consumption decisions, while the formation of consumption habits increases household propensity for precautionary savings.