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Optimal consumption and investment strategies with liquidity risk and lifetime uncertainty for Markov regime-switching jump diffusion models

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  • Jin, Zhuo
  • Liu, Guo
  • Yang, Hailiang

Abstract

In this paper, we consider the optimal consumption and investment strategies for households throughout their lifetime. Risks such as the illiquidity of assets, abrupt changes of market states, and lifetime uncertainty are considered. Taking the effects of heritage into account, investors are willing to limit their current consumption in exchange for greater wealth at their death, because they can take advantage of the higher expected returns of illiquid assets. Further, we model the liquidity risks in an illiquid market state by introducing frozen periods with uncertain lengths, during which investors cannot continuously rebalance their portfolios between different types of assets. In liquid market, investors can continuously remix their investment portfolios. In addition, a Markov regime-switching process is introduced to describe the changes in the market’s states. Jumps, classified as either moderate or severe, are jointly investigated with liquidity risks. Explicit forms of the optimal consumption and investment strategies are developed using the dynamic programming principle. Markov chain approximation methods are adopted to obtain the value function. Numerical examples demonstrate that the liquidity of assets and market states have significant effects on optimal consumption and investment strategies in various scenarios.

Suggested Citation

  • Jin, Zhuo & Liu, Guo & Yang, Hailiang, 2020. "Optimal consumption and investment strategies with liquidity risk and lifetime uncertainty for Markov regime-switching jump diffusion models," European Journal of Operational Research, Elsevier, vol. 280(3), pages 1130-1143.
    • Handle: RePEc:eee:ejores:v:280:y:2020:i:3:p:1130-1143
    DOI: 10.1016/j.ejor.2019.07.066
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    Cited by:

    1. Gaïgi, M’hamed & Ly Vath, Vathana & Scotti, Simone, 2022. "Optimal harvesting under marine reserves and uncertain environment," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1181-1194.
    2. Sarit Maitra & Vivek Mishra & Goutam Kr. Kundu & Kapil Arora, 2023. "Integration of Fractional Order Black-Scholes Merton with Neural Network," Papers 2310.04464, arXiv.org, revised Oct 2023.
    3. D'Auria, Bernardo & Salmerón Garrido, José Antonio, 2022. "An anticipative Markov modulated market," DES - Working Papers. Statistics and Econometrics. WS 34083, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. Liu, Guo & Jin, Zhuo & Li, Shuanming, 2021. "Household Lifetime Strategies under a Self-Contagious Market," European Journal of Operational Research, Elsevier, vol. 288(3), pages 935-952.
    5. Zhang, Xiang & Li, Lingfei & Zhang, Gongqiu, 2021. "Pricing American drawdown options under Markov models," European Journal of Operational Research, Elsevier, vol. 293(3), pages 1188-1205.
    6. Ailing Gu & Xinya He & Shumin Chen & Haixiang Yao, 2023. "Optimal Investment-Consumption and Life Insurance Strategy with Mispricing and Model Ambiguity," Methodology and Computing in Applied Probability, Springer, vol. 25(3), pages 1-19, September.
    7. Lesław Gajek & Marcin Rudź, 2020. "Finite-horizon general insolvency risk measures in a regime-switching Sparre Andersen model," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1507-1528, December.
    8. Wen Chen & Nicolas Langren'e, 2020. "Deep neural network for optimal retirement consumption in defined contribution pension system," Papers 2007.09911, arXiv.org, revised Jul 2020.
    9. 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.
    10. Deelstra, Griselda & Hieber, Peter, 2023. "Randomization and the valuation of guaranteed minimum death benefits," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1218-1236.
    11. Han, Jinhui & Li, Xiaolong & Ma, Guiyuan & Kennedy, Adrian Patrick, 2023. "Strategic trading with information acquisition and long-memory stochastic liquidity," European Journal of Operational Research, Elsevier, vol. 308(1), pages 480-495.
    12. Wen Chen & Nicolas Langrené, 2020. "Deep neural network for optimal retirement consumption in defined contribution pension system [Réseau de neurones profond pour consommation à la retraite optimale en système de retraite à cotisatio," Working Papers hal-02909818, HAL.

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