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Buy Low and Sell High
Min Dai National University of Singapore (NUS) - Department of Mathematics Hanqing Jin Mathematical Institute; Oxford-Man Institute of Quantitative Finance; St. Peter's College Yifei Zhong Mathematical Institute, University of Oxford Xun Yu Zhou University of Oxford - Nomura Centre for Mathematical Finance September 1, 2009 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.
Keywords: Black -- Scholes market, optimal stopping, stock goodness index, value function, free-boundary PDE (variational inequality) JEL Classifications: Q80, Q35, G60, G40, B91, B28 Working Paper SeriesDate posted: October 02, 2009 ; Last revised: October 02, 2009Suggested CitationContact Information
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