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Optimal investment and consumption decision of a family with life insurance

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  • Kwak, Minsuk
  • Shin, Yong Hyun
  • Choi, U Jin

Abstract

We study an optimal portfolio and consumption choice problem of a family that combines life insurance for parents who receive deterministic labor income until the fixed time T. We consider utility functions of parents and children separately and assume that parents have an uncertain lifetime. If parents die before time T, children have no labor income and they choose the optimal consumption and portfolio with remaining wealth and life insurance benefit. The object of the family is to maximize the weighted average of utility of parents and that of children. We obtain analytic solutions for the value function and the optimal policies, and then analyze how the changes of the weight of the parents' utility function and other factors affect the optimal policies.

Suggested Citation

  • Kwak, Minsuk & Shin, Yong Hyun & Choi, U Jin, 2011. "Optimal investment and consumption decision of a family with life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 176-188, March.
  • Handle: RePEc:eee:insuma:v:48:y:2011:i:2:p:176-188
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    References listed on IDEAS

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    3. Huiling Wu, 2016. "Optimal Investment-Consumption Strategy under Inflation in a Markovian Regime-Switching Market," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-17, July.
    4. 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.
    5. Erhan Bayraktar & Virginia Young, 2013. "Life Insurance Purchasing to Maximize Utility of Household Consumption," North American Actuarial Journal, Taylor & Francis Journals, vol. 17(2), pages 114-135.
    6. 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.
    7. Kiumars Sharifi & Saba Sharifi & Elnaz Rahrovy & Shima Shahmohammadi, 2013. "Examination and Determination of the Incentive Policies Effective In Increasing the Voluntary Insurance (Life Insurance) Demands In Tehran," International Journal of Learning and Development, Macrothink Institute, vol. 3(5), pages 1-14, October.
    8. 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.
    9. Wei-Ting Pan, 2016. "The Impact of Mandatory Savings on Life Cycle Consumption and Portfolio Choice," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 32, July-Dece.
    10. Jarner, Søren Fiig & Kronborg, Morten Tolver, 2016. "Entrance times of random walks: With applications to pension fund modeling," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 1-20.
    11. Chen, Chang-Chih & Chang, Chia-Chien & Sun, Edward W. & Yu, Min-Teh, 2022. "Optimal decision of dynamic wealth allocation with life insurance for mitigating health risk under market incompleteness," European Journal of Operational Research, Elsevier, vol. 300(2), pages 727-742.
    12. Rajat Deb & Kanchan Kumar Nath & Mukesh Nepal & Sourav Chakraborty & Kiran Sankar Chakraborty, 2021. "Do People Choose Life Insurance for Protection or for Saving?," Metamorphosis: A Journal of Management Research, , vol. 20(1), pages 35-44, June.
    13. Guambe, Calisto & Kufakunesu, Rodwell, 2015. "A note on optimal investment–consumption–insurance in a Lévy market," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 30-36.
    14. Schendel, Lorenz S., 2014. "Consumption-investment problems with stochastic mortality risk," SAFE Working Paper Series 43, Leibniz Institute for Financial Research SAFE.
    15. Kwak, Minsuk & Lim, Byung Hwa, 2014. "Optimal portfolio selection with life insurance under inflation risk," Journal of Banking & Finance, Elsevier, vol. 46(C), pages 59-71.
    16. Wei-Ting Pan, 2016. "The Impact of Mandatory Savings on Life Cycle Consumption and Portfolio Choice," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2016.
    17. Liang, Zongxia & Zhao, Xiaoyang, 2016. "Optimal mean–variance efficiency of a family with life insurance under inflation risk," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 164-178.

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