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Using Stochastic Approximation Algorithms in Stock Liquidation

In: Recent Developments In Mathematical Finance

Author

Listed:
  • G. Yin

    (Department of Mathematics, Wayne State University, Detroit, MI 48202, USA)

  • Q. Zhang

    (Department of Mathematics, University of Georgia, Athens, GA 30602, USA)

  • R.H. Liu

    (Department of Mathematics, University of Georgia, Athens, GA 30602, USA)

Abstract

For hybrid geometric Brownian motion stock liquidation models, it has been proved that the optimal selling policy is of threshold type, which can be obtained by solving a set of two-point boundary value problems. The total number of equations to be solved is the same as that of the numbers of states of the underlying Markov chain. To reduce the computational burden, this work develops Monte Carlo algorithms, which are recursive and are stochastic optimization type, to approximate the optimal threshold values in stock trading. Then asymptotic properties of the proposed algorithms such as the convergence and rates of convergence are developed.

Suggested Citation

  • G. Yin & Q. Zhang & R.H. Liu, 2001. "Using Stochastic Approximation Algorithms in Stock Liquidation," World Scientific Book Chapters, in: Jiongmin Yong (ed.), Recent Developments In Mathematical Finance, chapter 20, pages 238-248, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812799579_0020
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