Household consumption-investment-insurance decisions with uncertain income and market ambiguity

In this paper, we aim to study optimal decisions on consumption, investment and purchasing life insurance of a household with two consecutive generations, say parents and children. A continuous-time model featuring the impacts of labor income uncertainty and model uncertainty on those decisions is considered. Specifically, as in the economic literature about the labor income process, we consider the situation where the income growth rate is unobservable. The model takes account of the decision makings of both the parents and the children who are supposed to be ambiguity-averse expected utility maximizers. An attention is given to exploring the impacts of life insurance purchasing on the decision makings. The robustness approach to economic decision makings, which is implemented in the continuous-time model through a Girsanov's measure change for a Brownian motion, is applied to capture ambiguity aversion. Employing the known mathematical techniques in stochastic optimal control, say the Hamilton-Jacobi-Bellman dynamic programing principle, closed-form solutions are obtained. Numerical studies are provided to illustrate the economic implications of the solutions.