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Multiperiod Optimal Investment-Consumption Strategies with Mortality Risk and Environment Uncertainty

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  • Zhongfei Li
  • Ken Seng Tan
  • Hailiang Yang

Abstract

In this article we investigate three related investment-consumption problems for a risk-averse investor: (1) an investment-only problem that involves utility from only terminal wealth, (2) an investment-consumption problem that involves utility from only consumption, and (3) an extended investment-consumption problem that involves utility from both consumption and terminal wealth. Although these problems have been studied quite extensively in continuous-time frameworks, we focus on discrete time. Our contributions are (1) to model these investmentconsumption problems using a discrete model that incorporates the environment risk and mortality risk, in addition to the market risk that is typically considered, and (2) to derive explicit expressions of the optimal investment-consumption strategies to these modeled problems. Furthermore, economic implications of our results are presented. It is reassuring that many of our findings are consistent with the well-known results from the continuous-time models, even though our models have the additional features of modeling the environment uncertainty and the uncertain exit time.

Suggested Citation

  • Zhongfei Li & Ken Seng Tan & Hailiang Yang, 2008. "Multiperiod Optimal Investment-Consumption Strategies with Mortality Risk and Environment Uncertainty," North American Actuarial Journal, Taylor & Francis Journals, vol. 12(1), pages 47-64.
    • Handle: RePEc:taf:uaajxx:v:12:y:2008:i:1:p:47-64
    DOI: 10.1080/10920277.2008.10597499
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    Cited by:

    1. Lei He & Shuyi Zhou & Zilan Liu, 2020. "How is aggregate household consumption affected jointly by longevity, pension, and aging? Theory and evidence," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 67(4), pages 499-512, December.
    2. Weng, Chengguo, 2013. "Constant proportion portfolio insurance under a regime switching exponential Lévy process," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 508-521.
    3. Huiling Wu & Chengguo Weng & Yan Zeng, 2018. "Equilibrium consumption and portfolio decisions with stochastic discount rate and time-varying utility functions," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(2), pages 541-582, March.
    4. 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.
    5. Lei He & Shuyi Zhou & Zilan Liu, 0. "How is aggregate household consumption affected jointly by longevity, pension, and aging? Theory and evidence," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 0, pages 1-14.
    6. Bian, Lihua & Li, Zhongfei & Yao, Haixiang, 2018. "Pre-commitment and equilibrium investment strategies for the DC pension plan with regime switching and a return of premiums clause," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 78-94.
    7. Zeng, Yan & Wu, Huiling & Lai, Yongzeng, 2013. "Optimal investment and consumption strategies with state-dependent utility functions and uncertain time-horizon," Economic Modelling, Elsevier, vol. 33(C), pages 462-470.
    8. Cai, Jun & Ge, Chenliang, 2012. "Multi-objective private wealth allocation without subportfolios," Economic Modelling, Elsevier, vol. 29(3), pages 900-907.
    9. Yao, Haixiang & Li, Danping & Wu, Huiling, 2022. "Dynamic trading with uncertain exit time and transaction costs in a general Markov market," International Review of Financial Analysis, Elsevier, vol. 84(C).

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