Dynamic Portfolio Choice with Stochastic Wage and Life Insurance

We study optimal insurance, consumption and portfolio choice in a framework where a family purchases life insurance to protect the loss of the wage earner's human capital. Explicit solutions are obtained by employing CARA utility functions. We show that the optimal life insurance purchase is not a monotonic function of the correlation between the wage and the financial market. Meanwhile, the life insurance is explicitly affected by the family's risk preferences in general. The model also predicts that a family uses the life insurance and the investment together to hedge the risk from the stochastic wage