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Optimal portfolio selection with life insurance under inflation risk

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  • Kwak, Minsuk
  • Lim, Byung Hwa

Abstract

This paper investigates a continuous-time optimal consumption, investment, and life insurance decision problem of a family under inflation risk. In the financial market, there is a liquid inflation-linked index bond market which can be utilized to hedge the inflation risk. The explicit solutions are derived for constant relative risk aversion (CRRA) utility case by using martingale approach. The roles of index bond are investigated and it is verified that the index bond may have different roles depending on the market parameters. We analyze the effects of parameters on the optimal strategies with focus on the optimal demand for index bond and the optimal life insurance premium. Especially, the changes of expected inflation rate and volatility of inflation rate can have both positive and negative impacts on the life insurance premium and their quantitative impacts are considerable.

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  • 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.
    • Handle: RePEc:eee:jbfina:v:46:y:2014:i:c:p:59-71
    DOI: 10.1016/j.jbankfin.2014.04.019
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    Cited by:

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    3. Wael Hemrit, 2022. "Does insurance demand react to economic policy uncertainty and geopolitical risk? Evidence from Saudi Arabia," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 47(2), pages 460-492, April.
    4. Agnieszka Konicz & David Pisinger & Alex Weissensteiner, 2015. "Optimal annuity portfolio under inflation risk," Computational Management Science, Springer, vol. 12(3), pages 461-488, July.
    5. Srbinoski Bojan & Strozzi Fernanda & Poposki Klime & Born Patricia H., 2020. "Trends in Life Insurance Demand and Lapse Literature," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 14(2), pages 1-46, July.
    6. Lu, Jin-Ray & Hwang, Chih-Chiang & Liu, Min-Luan & Lin, Chien-Yi, 2016. "An incentive problem of risk balancing in portfolio choices," The Quarterly Review of Economics and Finance, Elsevier, vol. 61(C), pages 192-200.
    7. Lim, Byung Hwa & Kwak, Minsuk, 2016. "Bequest motive and incentive to retire: Consumption, investment, retirement, and life insurance strategies," Finance Research Letters, Elsevier, vol. 16(C), pages 19-27.
    8. 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.
    9. 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.
    10. Huang, Zongyuan & Wang, Haiyang & Wu, Zhen, 2020. "A kind of optimal investment problem under inflation and uncertain time horizon," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    11. 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.
    12. Guan, Guohui & Liang, Zongxia, 2016. "A stochastic Nash equilibrium portfolio game between two DC pension funds," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 237-244.
    13. Spyros Papathanasiou & Dimitris Kenourgios & Drosos Koutsokostas & Georgios Pergeris, 2023. "Can treasury inflation-protected securities safeguard investors from outward risk spillovers? A portfolio hedging strategy through the prism of COVID-19," Journal of Asset Management, Palgrave Macmillan, vol. 24(3), pages 198-211, May.
    14. Menoncin, Francesco & Regis, Luca, 2017. "Longevity-linked assets and pre-retirement consumption/portfolio decisions," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 75-86.
    15. 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.
    16. Guan, Guohui & Liang, Zongxia & Xia, Yi, 2023. "Optimal management of DC pension fund under the relative performance ratio and VaR constraint," European Journal of Operational Research, Elsevier, vol. 305(2), pages 868-886.
    17. Guohui Guan, 2020. "Equilibrium and Precommitment Mean-Variance Portfolio Selection Problem with Partially Observed Price Index and Multiple Assets," Methodology and Computing in Applied Probability, Springer, vol. 22(1), pages 25-47, March.
    18. 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.
    19. Wenyuan Li & Pengyu Wei, 2024. "Optimal life insurance and annuity decision under money illusion," Papers 2410.20128, arXiv.org.
    20. Francesco Menoncin & Luca Regis, 2015. "Longevity assets and pre-retirement consumption/portfolio decisions," Working Papers 2/2015, IMT School for Advanced Studies Lucca, revised May 2015.
    21. 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.
    22. Esfandi, Elaheh & Mousavi, Mir Hossein & Moshrefi, Rassam & Farhang-Moghaddam, Babak, 2020. "Insurer Optimal Asset Allocation in a Small and Closed Economy: The Case of Iran’s Social Security Organization," Journal of Money and Economy, Monetary and Banking Research Institute, Central Bank of the Islamic Republic of Iran, vol. 15(4), pages 445-461, October.
    23. Dunbar, Kwamie & Owusu-Amoako, Johnson, 2023. "Predicting inflation expectations: A habit-based explanation under hedging," International Review of Financial Analysis, Elsevier, vol. 89(C).

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    More about this item

    Keywords

    Optimal consumption/investment; Inflation risk; Index bond; Life insurance;
    All these keywords.

    JEL classification:

    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • 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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