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Portfolio choice, portfolio liquidation, and portfolio transition under drift uncertainty

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  • Alexis Bismuth
  • Olivier Gu'eant
  • Jiang Pu

Abstract

This paper presents several models addressing optimal portfolio choice, optimal portfolio liquidation, and optimal portfolio transition issues, in which the expected returns of risky assets are unknown. Our approach is based on a coupling between Bayesian learning and dynamic programming techniques that leads to partial differential equations. It enables to recover the well-known results of Karatzas and Zhao in a framework \`a la Merton, but also to deal with cases where martingale methods are no longer available. In particular, we address optimal portfolio choice, portfolio liquidation, and portfolio transition problems in a framework \`a la Almgren-Chriss, and we build therefore a model in which the agent takes into account in his decision process both the liquidity of assets and the uncertainty with respect to their expected return.

Suggested Citation

  • Alexis Bismuth & Olivier Gu'eant & Jiang Pu, 2016. "Portfolio choice, portfolio liquidation, and portfolio transition under drift uncertainty," Papers 1611.07843, arXiv.org, revised Mar 2019.
    • Handle: RePEc:arx:papers:1611.07843
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    References listed on IDEAS

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    1. Olivier Guéant & Jiang Pu & Guillaume Royer, 2015. "Accelerated Share Repurchase: Pricing And Execution Strategy," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(03), pages 1-31.
    2. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    3. Paul A. Samuelson, 2011. "Lifetime Portfolio Selection by Dynamic Stochastic Programming," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 31, pages 465-472, World Scientific Publishing Co. Pte. Ltd..
    4. Olivier Guéant, 2015. "Optimal Execution and Block Trade Pricing: A General Framework," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(4), pages 336-365, September.
    5. J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 25(2), pages 65-86.
    6. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    7. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.
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    Citations

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    Cited by:

    1. Felix Dammann & Giorgio Ferrari, 2023. "Optimal execution with multiplicative price impact and incomplete information on the return," Finance and Stochastics, Springer, vol. 27(3), pages 713-768, July.
    2. Shubhangi Sikaria & Rituparna Sen & Neelesh S. Upadhye, 2019. "Bayesian Filtering for Multi-period Mean-Variance Portfolio Selection," Papers 1911.07526, arXiv.org, revised Aug 2020.
    3. Felix Dammann & Giorgio Ferrari, 2022. "Optimal Execution with Multiplicative Price Impact and Incomplete Information on the Return," Papers 2202.10414, arXiv.org, revised Nov 2022.
    4. Dongmei Zhu & Harry Zheng, 2022. "Effective Approximation Methods for Constrained Utility Maximization with Drift Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 194(1), pages 191-219, July.
    5. Andrea Mazzon & Peter Tankov, 2024. "Optimal stopping and divestment timing under scenario ambiguity and learning," Papers 2408.09349, arXiv.org, revised Oct 2024.
    6. Gao, Shuping & Guo, Junyi & Liang, Xiaoqing, 2025. "Bayesian adaptive portfolio optimization for DC pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 122(C), pages 262-274.
    7. Horst, Ulrich & Xia, Xiaonyu & Zhou, Chao, 2021. "Portfolio Liquidation under Factor Uncertainty," Rationality and Competition Discussion Paper Series 274, CRC TRR 190 Rationality and Competition.
    8. Dammann, Felix & Ferrari, Giorgio, 2022. "Optimal Execution with Multiplicative Price Impact and Incomplete Information on the Return," Center for Mathematical Economics Working Papers 663, Center for Mathematical Economics, Bielefeld University.
    9. Fayc{c}al Drissi, 2022. "Solvability of Differential Riccati Equations and Applications to Algorithmic Trading with Signals," Papers 2202.07478, arXiv.org, revised Aug 2023.
    10. Qixuan Luo & Shijia Song & Handong Li, 2023. "Research on the Effects of Liquidation Strategies in the Multi-asset Artificial Market," Computational Economics, Springer;Society for Computational Economics, vol. 62(4), pages 1721-1750, December.
    11. Carmine De Franco & Johann Nicolle & Huy^en Pham, 2020. "Discrete-time portfolio optimization under maximum drawdown constraint with partial information and deep learning resolution," Papers 2010.15779, arXiv.org, revised Oct 2020.
    12. Philippe Bergault & Fayc{c}al Drissi & Olivier Gu'eant, 2021. "Multi-asset optimal execution and statistical arbitrage strategies under Ornstein-Uhlenbeck dynamics," Papers 2103.13773, arXiv.org, revised Mar 2022.
    13. Ulrich Horst & Xiaonyu Xia & Chao Zhou, 2019. "Portfolio liquidation under factor uncertainty," Papers 1909.00748, arXiv.org.

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