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Pre-commitment vs. time-consistent strategies for the generalized multi-period portfolio optimization with stochastic cash flows

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  • Zhou, Zhongbao
  • Xiao, Helu
  • Yin, Jialing
  • Zeng, Ximei
  • Lin, Ling

Abstract

In this paper, we propose a multi-period portfolio optimization model with stochastic cash flows. Under the mean–variance preference, we derive the pre-commitment and time-consistent investment strategies by applying the embedding scheme and backward induction approach, respectively. We show that the time-consistent strategy is identical to the optimal open-loop strategy. Also, under the exponential utility preference, we develop the optimal strategy for multi-period investment, which is time-consistent. We show that the above two time-consistent strategies are equivalent in some cases. We compare the pre-commitment and time-consistent strategies under different situations with some numerical simulations. The results indicate that the time-consistent strategy is more stable and secure than pre-commitment strategy under the generalized mean–variance criterion.

Suggested Citation

  • Zhou, Zhongbao & Xiao, Helu & Yin, Jialing & Zeng, Ximei & Lin, Ling, 2016. "Pre-commitment vs. time-consistent strategies for the generalized multi-period portfolio optimization with stochastic cash flows," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 187-202.
    • Handle: RePEc:eee:insuma:v:68:y:2016:i:c:p:187-202
    DOI: 10.1016/j.insmatheco.2016.03.002
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    Cited by:

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    3. Helu Xiao & Tiantian Ren & Yanfei Bai & Zhongbao Zhou, 2019. "Time-Consistent Investment-Reinsurance Strategies for the Insurer and the Reinsurer under the Generalized Mean-Variance Criteria," Mathematics, MDPI, vol. 7(9), pages 1-25, September.
    4. Helu Xiao & Tiantian Ren & Zhongbao Zhou, 2019. "Time-Consistent Strategies for the Generalized Multiperiod Mean-Variance Portfolio Optimization Considering Benchmark Orientation," Mathematics, MDPI, vol. 7(8), pages 1-26, August.
    5. Yanfei Bai & Zhongbao Zhou & Rui Gao & Helu Xiao, 2020. "Nash Equilibrium Investment-Reinsurance Strategies for an Insurer and a Reinsurer with Intertemporal Restrictions and Common Interests," Mathematics, MDPI, vol. 8(1), pages 1-26, January.
    6. Zhang, Jingong & Tan, Ken Seng & Weng, Chengguo, 2017. "Optimal hedging with basis risk under mean–variance criterion," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 1-15.

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