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Optimal Portfolio Liquidation and Dynamic Mean-variance Criterion

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  • Jia-Wen Gu
  • Mogens Steffensen

Abstract

In this paper, we consider the optimal portfolio liquidation problem under the dynamic mean-variance criterion and derive time-consistent solutions in three important models. We give adapted optimal strategies under a reconsidered mean-variance subject at any point in time. We get explicit trading strategies in the basic model and when random pricing signals are incorporated. When we consider stochastic liquidity and volatility, we construct a generalized HJB equation under general assumptions for the parameters. We obtain an explicit solution in stochastic volatility model with a given structure supported by empirical studies.

Suggested Citation

  • Jia-Wen Gu & Mogens Steffensen, 2015. "Optimal Portfolio Liquidation and Dynamic Mean-variance Criterion," Papers 1510.09110, arXiv.org.
    • Handle: RePEc:arx:papers:1510.09110
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    File URL: http://arxiv.org/pdf/1510.09110
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    References listed on IDEAS

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    1. Jones, Charles M & Kaul, Gautam & Lipson, Marc L, 1994. "Transactions, Volume, and Volatility," The Review of Financial Studies, Society for Financial Studies, vol. 7(4), pages 631-651.
    2. Marcel Blais & Philip Protter, 2010. "An Analysis Of The Supply Curve For Liquidity Risk Through Book Data," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(06), pages 821-838.
    3. Suominen, Matti, 2001. "Trading Volume and Information Revelation in Stock Market," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 36(4), pages 545-565, December.
    4. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    5. Ralf Korn, 1997. "Some applications of L2-hedging with a non-negative wealth process," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(1), pages 65-79.
    6. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    7. Carhart, Mark M, 1997. "On Persistence in Mutual Fund Performance," Journal of Finance, American Finance Association, vol. 52(1), pages 57-82, March.
    8. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    9. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
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    Cited by:

    1. Dong-Mei Zhu & Jia-Wen Gu & Feng-Hui Yu & Tak-Kuen Siu & Wai-Ki Ching, 2021. "Optimal pairs trading with dynamic mean-variance objective," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(1), pages 145-168, August.

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