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

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  • Ning Wang
  • Zhuo Jin
  • Tak Kuen Siu
  • Ming Qiu

Abstract

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.

Suggested Citation

  • Ning Wang & Zhuo Jin & Tak Kuen Siu & Ming Qiu, 2021. "Household consumption-investment-insurance decisions with uncertain income and market ambiguity," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2021(10), pages 832-865, November.
    • Handle: RePEc:taf:sactxx:v:2021:y:2021:i:10:p:832-865
    DOI: 10.1080/03461238.2021.1886981
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    Cited by:

    1. Yang Wang & Jianwei Lin & Dandan Chen & Jizhou Zhang, 2023. "Optimal Investment–Consumption–Insurance Problem of a Family with Stochastic Income under the Exponential O-U Model," Mathematics, MDPI, vol. 11(19), pages 1-19, October.
    2. Ailing Gu & Xinya He & Shumin Chen & Haixiang Yao, 2023. "Optimal Investment-Consumption and Life Insurance Strategy with Mispricing and Model Ambiguity," Methodology and Computing in Applied Probability, Springer, vol. 25(3), pages 1-19, September.
    3. Rui Jiao & Wei Liu & Yijun Hu, 2023. "The Optimal Consumption, Investment and Life Insurance for Wage Earners under Inside Information and Inflation," Mathematics, MDPI, vol. 11(15), pages 1-18, August.

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