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

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  • Zhen Zhao
  • Wei Liu
  • Xiaoyi Tang

Abstract

This article 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 wage earner. 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 wage earner is alive or not, we formulate and solve the corresponding Hamilton-Jacobi-Bellman (HJB) equations for the two scenarios of wage earner survival and wage earner’s demise, respectively, and obtain explicit expressions for the optimal investment, consumption, and life insurance strategies of households. Through sensitivity analysis of important parameters, 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.

Suggested Citation

  • Zhen Zhao & Wei Liu & Xiaoyi Tang, 2025. "Optimal investment, consumption, and life insurance decisions for households with consumption habits under the health shock risk," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 54(15), pages 4766-4790, August.
    • Handle: RePEc:taf:lstaxx:v:54:y:2025:i:15:p:4766-4790
    DOI: 10.1080/03610926.2024.2427232
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