2024/02/01 by Zhen Zhao, Wei Liu, Zhao, Zhen +3
Economics, Econometrics and Finance · #Applications (stat.AP) #FOS: Computer and information sciences #Insurance and Financial Risk Management
paper · pdf · doi:10.48550/arxiv.2402.00440
openalex publication_date 2024/02/01 · openalex created_date 2024/02/03 · openalex updated_date 2026/07/28
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.