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

Ning Wang, Zhuo Jin*, Tak Kuen Siu, Ming Qiu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)832-865
Number of pages34
JournalScandinavian Actuarial Journal
Issue number10
Early online date23 Feb 2021
Publication statusPublished - 26 Nov 2021


  • Investment
  • consumption
  • life insurance
  • model uncertainty
  • stochastic income growth
  • two consecutive generations


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