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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.

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  • 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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    5. Liu, Guo & Jin, Zhuo & Li, Shuanming, 2021. "Household Lifetime Strategies under a Self-Contagious Market," European Journal of Operational Research, Elsevier, vol. 288(3), pages 935-952.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Schendel, Lorenz S., 2014. "Consumption-investment problems with stochastic mortality risk," SAFE Working Paper Series 43, Leibniz Institute for Financial Research SAFE.
    11. Wenyuan Li & Pengyu Wei, 2024. "Optimal life insurance and annuity decision under money illusion," Papers 2410.20128, arXiv.org.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    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, January-A.
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    18. 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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