Utility maximization of a household with smooth ambiguity and consumption habit

Abstract

This paper investigates optimal consumption, investment and life insurance decisions for a two-generation household incorporating smooth ambiguity and consumption habit formation. The household invests in a financial market consisting of a risk-free asset and a risky asset, where ambiguity arises from an unknown market price of risk. Habit formation depends on historical consumption and satisfies an ordinary differential equation. Moreover, the parent faces mortality risk, which can be hedged by life insurance. The household aims to maximize the total expected utility of consumption, bequest and terminal wealth. By utilizing the mean-field type control and dynamic programming techniques, we derive the extended Hamilton–Jacobi–Bellman equations and obtain the optimal strategies. Numerical experiments illustrate the effects of ambiguity aversion and consumption habit on the equilibrium strategies. The results indicate that higher level of the child’s ambiguity aversion and risk aversion lead to lower investment and life insurance purchase by the parent, with the effect on insurance demand being more pronounced than on investment.