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Optimal consumption–investment and life-insurance purchase strategy for couples with correlated lifetimes

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  • Wei, Jiaqin
  • Cheng, Xiang
  • Jin, Zhuo
  • Wang, Hao

Abstract

This paper presents a technique to solve the problem where a couple aims to optimize their consumption, investment, and life-insurance purchasing strategies, thereby maximizing their family objective until retirement. Assumed correlated lifetimes of the two wage earners are modeled by using both the copula and common-shock models. Subsequently, closed-form solutions are obtained for determination of the optimal strategies in both the copula and a special case of the common-shock models. As observed, use of the copula model is more advantageous in its provision of closed-form strategies and ability to distinguish mortality impacts. The optimization problem considered herein is investigated under a Markovian setting and solved using the Hamilton–Jacobi–Bellman equation. Numerical examples are also provided to illustrate the utility of the proposed optimization strategy.

Suggested Citation

  • Wei, Jiaqin & Cheng, Xiang & Jin, Zhuo & Wang, Hao, 2020. "Optimal consumption–investment and life-insurance purchase strategy for couples with correlated lifetimes," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 244-256.
    • Handle: RePEc:eee:insuma:v:91:y:2020:i:c:p:244-256
    DOI: 10.1016/j.insmatheco.2020.02.006
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    References listed on IDEAS

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    Cited by:

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    2. 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.
    3. 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.
    4. 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.
    5. Park, Kyunghyun & Wong, Hoi Ying & Yan, Tingjin, 2023. "Robust retirement and life insurance with inflation risk and model ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 1-30.

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