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Optimal asset allocation for households with healthcare and insurance

Abstract
This paper studies an optimal consumption, life insurance, investment, and healthcare spending problem for a two-member household with constant relative risk aversion (CRRA) preferences. Healthcare spending slows down the natural growth of the mortality rate, thereby extending the life expectancy of family members. We take into account the trade-off between the costly health investment and the breadwinner's life insurance. Analytical solutions are derived using the dynamic programming method. Additionally, numerical examples are presented to illustrate our results.  It shows that healthcare spending steadily increases with age and reduces the household's reliance on life insurance. The ratio of insurance to healthcare spending decreases with both age and the healthcare efficacy function parameter. Moreover, the higher natural growth rate of mortality leads to a more stable increase in healthcare spending with age.