Optimal Investment, Consumption, and Life Insurance Choices with Habit Formation and Inflation Risk

This research studies the optimal consumption, investment, and life insurance choices for a wage earner with habit formation, inflation risk, and mortality risk. The wage earner has access to a risk-free asset, an index bond, and a stock in a financial market. The index bond hedges inflation risk, while life insurance hedges mortality risk. The aim of the wage earner is to maximize the expected utility of consumption, bequest, and terminal wealth, where the utility of consumption comes from the part of the consumption that exceeds a minimum consumption requirement given by the habit level. By using the dynamic programming method, we provide and prove a verification theorem and obtain closed-form expressions for the value function, the optimal life insurance premium rate, and the optimal investment and consumption strategies. Numerical results reveal that habit formation and mortality force change play important roles in the financial behaviors of the wage earner. Especially, the impacts of the expected inflation rate and consumption habit on the optimal strategies are mutual restraint; increasing mortality force raises the demand for life insurance; and the effects of other parameters are also affected by consumption habit and mortality force change.