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Optimal Decision for Selling an Illiquid Stock

Author

Listed:
  • Baojun Bian

    (Tongji University)

  • Min Dai

    (National University of Singapore (NUS))

  • Lishang Jiang

    (Tongji University)

  • Qing Zhang

    (The University of Georgia)

  • Yifei Zhong

    (Oxford University)

Abstract

This paper is concerned with liquidation of an illiquid stock. The stock price follows a fluid model which is dictated by the rates of selling and buying over time. The objective is to maximize the expected overall return. The method of constrained viscosity solution is used to characterize the dynamics governing the optimal reward function and the associated boundary conditions. Numerical examples are given to illustrate the results.

Suggested Citation

  • Baojun Bian & Min Dai & Lishang Jiang & Qing Zhang & Yifei Zhong, 2011. "Optimal Decision for Selling an Illiquid Stock," Journal of Optimization Theory and Applications, Springer, vol. 151(2), pages 402-417, November.
    • Handle: RePEc:spr:joptap:v:151:y:2011:i:2:d:10.1007_s10957-011-9897-0
    DOI: 10.1007/s10957-011-9897-0
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    References listed on IDEAS

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    1. Dai, Min & Kwok, Yue Kuen & You, Hong, 2007. "Intensity-based framework and penalty formulation of optimal stopping problems," Journal of Economic Dynamics and Control, Elsevier, vol. 31(12), pages 3860-3880, December.
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    3. Longstaff, Francis A, 2001. "Optimal Portfolio Choice and the Valuation of Illiquid Securities," The Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 407-431.
    4. Pemy, M. & Zhang, Q. & Yin, G., 2007. "Liquidation of a large block of stock," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1295-1305, May.
    5. Ajay Subramanian & Robert A. Jarrow, 2001. "The Liquidity Discount," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 447-474, October.
    6. Robert Almgren, 2003. "Optimal execution with nonlinear impact functions and trading-enhanced risk," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(1), pages 1-18.
    7. Min Dai & Yue Kuen Kwok & Jianping Zong, 2008. "Guaranteed Minimum Withdrawal Benefit In Variable Annuities," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 595-611, October.
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    Cited by:

    1. Hidekazu Yoshioka & Yuta Yaegashi, 2020. "A growth rate control problem of harmful species population and its application to algae bloom," Environment Systems and Decisions, Springer, vol. 40(1), pages 107-124, March.

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