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Buy Low and Sell High

In: Contemporary Quantitative Finance

Author

Listed:
  • Min Dai

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

  • Hanqing Jin

    (The University of Oxford, Mathematical Institute and Nomura Centre for Mathematical Finance, and Oxford-Man Institute of Quantitative Finance)

  • Yifei Zhong

    (The University of Oxford, Mathematical Institute and Nomura Centre for Mathematical Finance, and Oxford-Man Institute of Quantitative Finance)

  • Xun Yu Zhou

    (The University of Oxford, Mathematical Institute and Nomura Centre for Mathematical Finance, and Oxford-Man Institute of Quantitative Finance
    The Chinese University of Hong Kong, Department of Systems Engineering and Engineering Management)

Abstract

In trading stocks investors naturally aspire to “buy low and sell high (BLSH)”. This paper formalizes the notion of BLSH by formulating stock buying/selling in terms of four optimal stopping problems involving the global maximum and minimum of the stock prices over a given investment horizon. Assuming that the stock price process follows a geometric Brownian motion, all the four problems are solved and buying/selling strategies completely characterized via a free-boundary PDE approach.

Suggested Citation

  • Min Dai & Hanqing Jin & Yifei Zhong & Xun Yu Zhou, 2010. "Buy Low and Sell High," Springer Books, in: Carl Chiarella & Alexander Novikov (ed.), Contemporary Quantitative Finance, pages 317-333, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-03479-4_16
    DOI: 10.1007/978-3-642-03479-4_16
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