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Dynamic portfolio optimization with liquidity cost and market impact: a simulation-and-regression approach

Author

Listed:
  • Rongju Zhang
  • Nicolas Langrené
  • Yu Tian
  • Zili Zhu
  • Fima Klebaner
  • Kais Hamza

Abstract

We present a simulation-and-regression method for solving dynamic portfolio optimization problems in the presence of general transaction costs, liquidity costs and market impact. This method extends the classical least squares Monte Carlo algorithm to incorporate switching costs, corresponding to transaction costs and transient liquidity costs, as well as multiple endogenous state variables, namely the portfolio value and the asset prices subject to permanent market impact. To handle endogenous state variables, we adapt a control randomization approach to portfolio optimization problems and further improve the numerical accuracy of this technique for the case of discrete controls. We validate our modified numerical method by solving a realistic cash-and-stock portfolio with a power-law liquidity model. We identify the certainty equivalent losses associated with ignoring liquidity effects, and illustrate how our dynamic optimization method protects the investor's capital under illiquid market conditions. Lastly, we analyze, under different liquidity conditions, the sensitivities of certainty equivalent returns and optimal allocations with respect to trading volume, stock price volatility, initial investment amount, risk aversion level and investment horizon.

Suggested Citation

  • Rongju Zhang & Nicolas Langrené & Yu Tian & Zili Zhu & Fima Klebaner & Kais Hamza, 2019. "Dynamic portfolio optimization with liquidity cost and market impact: a simulation-and-regression approach," Quantitative Finance, Taylor & Francis Journals, vol. 19(3), pages 519-532, March.
    • Handle: RePEc:taf:quantf:v:19:y:2019:i:3:p:519-532
    DOI: 10.1080/14697688.2018.1524155
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    Cited by:

    1. Qi Deng & Zhong-guo Zhou, 2024. "Liquidity Jump, Liquidity Diffusion, and Portfolio of Assets with Extreme Liquidity," Papers 2407.00813, arXiv.org.
    2. Ivan Guo & Nicolas Langrené & Gregoire Loeper & Wei Ning, 2020. "Robust utility maximization under model uncertainty via a penalization approach," Working Papers hal-02910261, HAL.
    3. Rongju Zhang & Nicolas Langrené & Yu Tian & Zili Zhu & Fima Klebaner & Kais Hamza, 2019. "Skewed target range strategy for multiperiod portfolio optimization using a two-stage least squares Monte Carlo method," Post-Print hal-02909342, HAL.
    4. repec:tin:wpaper:20230016 is not listed on IDEAS
    5. Chen, Shun & Ge, Lei, 2021. "A learning-based strategy for portfolio selection," International Review of Economics & Finance, Elsevier, vol. 71(C), pages 936-942.

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