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Optimal Decision for Selling an Illiquid Stock

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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.

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Authors and Affiliations

  1. Department of Mathematics, Tongji University, Shanghai, China

    Baojun Bian & Lishang Jiang

  2. Department of Mathematics, National University of Singapore (NUS), Singapore, Singapore

    Min Dai

  3. Department of Mathematics, The University of Georgia, Athens, GA, USA

    Qing Zhang

  4. Mathematical Institute and Oxford-Man Institute of Quantitative Finance, Oxford University, Oxford, UK

    Yifei Zhong

Authors
  1. Baojun Bian
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  2. Min Dai
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  3. Lishang Jiang
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  4. Qing Zhang
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  5. Yifei Zhong
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Correspondence to Qing Zhang.

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Bian, B., Dai, M., Jiang, L. et al. Optimal Decision for Selling an Illiquid Stock. J Optim Theory Appl 151, 402–417 (2011). https://doi.org/10.1007/s10957-011-9897-0

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  • DOI: https://doi.org/10.1007/s10957-011-9897-0

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