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Optimal consumption, portfolio, and life insurance policies under interest rate and inflation risks

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  • Han, Nan-Wei
  • Hung, Mao-Wei

Abstract

This paper solves the optimal life insurance, consumption, and portfolio decisions of a wage earner before retirement under interest rate and inflation risks. The wage earner’s preferences are represented by the stochastic differential utility, which separates the coefficient of relative risk aversion from the elasticity of intertemporal substitution (EIS). The wage earner’s life insurance demand is affected by the volatile interest rates and inflation. The optimal life insurance demand decreases with the level of nominal interest rates. Under an assumption of deterministic nominal income, the demand for life insurance would not be affected by the level of inflation. However, if the wage earner’s income is indexed to inflation, the life insurance demand would increase with the level of inflation. Furthermore, under investment opportunities with greater volatilities, wage earners who optimally allocate their wealth to the financial market benefit more from financial investments and cut their demand for life insurance. An analysis of EIS and risk aversion on life insurance demand shows that the demand for life insurance over the planning horizon increases with the measure of relative risk aversion but decreases with EIS. Optimal consumption is affected by the insurance premium load and the direction depends on the size of EIS relative to unity.

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  • Han, Nan-Wei & Hung, Mao-Wei, 2017. "Optimal consumption, portfolio, and life insurance policies under interest rate and inflation risks," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 54-67.
    • Handle: RePEc:eee:insuma:v:73:y:2017:i:c:p:54-67
    DOI: 10.1016/j.insmatheco.2017.01.004
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    3. Eling, Martin & Ghavibazoo, Omid & Hanewald, Katja, 2021. "Willingness to take financial risks and insurance holdings: A European survey," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 95(C).
    4. 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.
    5. Xiaoyi Zhang & Junyi Guo, 2018. "The Role of Inflation-Indexed Bond in Optimal Management of Defined Contribution Pension Plan During the Decumulation Phase," Risks, MDPI, vol. 6(2), pages 1-16, March.
    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. 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.
    8. Calisto Guambe & Rodwell Kufakunesu, 2017. "Optimal investment-consumption and life insurance selection problem under inflation. A BSDE approach," Papers 1711.01760, arXiv.org.
    9. 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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    More about this item

    Keywords

    Life insurance; Stochastic differential utility; Interest rate risk; Inflation; Elasticity of intertemporal substitution; Risk aversion;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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