Optimal portfolio selection with life insurance under subjective survival belief and habit formation

This paper studies the optimal consumption, investment, and life insurance choices for a wage earner with subjective survival beliefs and habit formation types. The wage-earner has access to a risk-free asset, an index bond, and a stock in a financial market. Introducing subjective survival beliefs describes the wage earner's optimistic or pessimistic attitude towards the longevity risk. Two types of habit formation are considered: one depends on real past consumption; the other is incited by money illusion and depends on nominal past consumption. The aim is to maximize the expected utility of real consumption, total legacy, and terminal wealth, where the utility of consumption comes from the part of real consumption that exceeds real habit level. Using the dynamic programming method, we provide and prove a verification theorem and obtain the closed-form solution of the optimization problem. Numerical results reveal that subjective survival beliefs and habit formation types play important roles in the financial behaviors of the wage-earner. Detailed results are exhibited. Especially, subjective survival beliefs, the existence of habit formation, and the relative risk aversion coefficient affect the demand for life insurance.