  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.
