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Optimal mean–variance efficiency of a family with life insurance under inflation risk

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  • Liang, Zongxia
  • Zhao, Xiaoyang

Abstract

We study an optimization problem of a family under mean–variance efficiency. The market consists of cash, a zero-coupon bond, an inflation-indexed zero-coupon bond, a stock, life insurance and income-replacement insurance. The instantaneous interest rate is modeled as the Cox–Ingersoll–Ross (CIR) model, and we use a generalized Black–Scholes model to characterize the stock and labor income. We also take into account the inflation risk and consider our problem in the real market. The goal of the family is to maximize the mean of the surplus wealth at the retirement or death of the breadwinner and minimize its variance by finding a portfolio selection. The efficient frontier and optimal strategies are derived through the dynamic programming method and the technique of solving associated nonlinear HJB equations. We also present a numerical illustration to explore the impact of economical parameters on the efficient frontier.

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  • 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.
    • Handle: RePEc:eee:insuma:v:71:y:2016:i:c:p:164-178
    DOI: 10.1016/j.insmatheco.2016.09.004
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    Cited by:

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    2. Liu, Guo & Jin, Zhuo & Li, Shuanming, 2021. "Optimal investment, consumption, and life insurance strategies under a mutual-exciting contagious market," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 508-524.
    3. 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.
    4. 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.

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    More about this item

    Keywords

    IE13; IM12; IE43; IE53; IB12; Mean–variance efficiency; Surplus wealth of the family; Income-replacement insurance; Lagrange dual method; Replication of assets; Dynamic programming; Nonlinear HJB equations;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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