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Life Insurance Purchasing to Maximize Utility of Household Consumption

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  • Erhan Bayraktar
  • Virginia R. Young

Abstract

We determine the optimal amount of life insurance for a household of two wage earners. We consider the simple case of exponential utility, thereby removing wealth as a factor in buying life insurance, while retaining the relationship among life insurance, income, and the probability of dying and thus losing that income. For insurance purchased via a single premium or premium payable continuously, we explicitly determine the optimal death benefit. We show that if the premium is determined to target a specific probability of loss per policy, then the rates of consumption are identical under single premium or continuously payable premium. Thus, not only is equivalence of consumption achieved for the households under the two premium schemes, it is also obtained for the insurance company in the sense of equivalence of loss probabilities.

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  • Erhan Bayraktar & Virginia R. Young, 2012. "Life Insurance Purchasing to Maximize Utility of Household Consumption," Papers 1205.5958, arXiv.org, revised Jun 2013.
    • Handle: RePEc:arx:papers:1205.5958
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    References listed on IDEAS

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    1. Richard, Scott F., 1975. "Optimal consumption, portfolio and life insurance rules for an uncertain lived individual in a continuous time model," Journal of Financial Economics, Elsevier, vol. 2(2), pages 187-203, June.
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    11. Nielsen, Peter Holm & Steffensen, Mogens, 2008. "Optimal investment and life insurance strategies under minimum and maximum constraints," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 15-28, August.
    12. Pliska, Stanley R. & Ye, Jinchun, 2007. "Optimal life insurance purchase and consumption/investment under uncertain lifetime," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1307-1319, May.
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    Cited by:

    1. An Chen & Giorgio Ferrari & Shihao Zhu, 2023. "Striking the Balance: Life Insurance Timing and Asset Allocation in Financial Planning," Papers 2312.02943, arXiv.org.
    2. 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.
    3. Erhan Bayraktar & S. David Promislow & Virginia R. Young, 2015. "Purchasing Term Life Insurance to Reach a Bequest Goal: Time-Dependent Case," North American Actuarial Journal, Taylor & Francis Journals, vol. 19(3), pages 224-236, July.
    4. Liang, Xiaoqing & Young, Virginia R., 2018. "Annuitization and asset allocation under exponential utility," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 167-183.
    5. Erhan Bayraktar & David Promislow & Virginia Young, 2014. "Purchasing Term Life Insurance to Reach a Bequest Goal while Consuming," Papers 1412.2262, arXiv.org, revised Feb 2016.
    6. Bayraktar, Erhan & Promislow, S. David & Young, Virginia R., 2014. "Purchasing life insurance to reach a bequest goal," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 204-216.
    7. Chen, An & Ferrari, Giorgio & Zhu, Shihao, 2023. "Striking the Balance: Life Insurance Timing and Asset Allocation in Financial Planning," Center for Mathematical Economics Working Papers 684, Center for Mathematical Economics, Bielefeld University.

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