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.
Min Dai is an affiliated member of Risk Management Institute of NUS.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Brezis, H., Friedman, A.: Estimates on the support of solutions of parabolic variational inequalities. Ill. J. Math. 20, 82–97 (1976)
Dai, M., Kwok, Y.K., Wu, L.: Optimal shouting policies of options with strike reset rights. Math. Finance 14(3), 383–401 (2004)
Dai, M., Zhong, Y.: Optimal stock selling/buying strategy with reference to the ultimate average. Working Paper, National University of Singapore (2008)
du Toit, J., Peskir, G.: Selling a stock at the ultimate maximum. Ann. Appl. Probab. 19, 983–1014 (2009)
Friedman, A.: Variational Principles and Free Boundary Problems. Wiley, New York (1982)
Shiryaev, A.: Quickest detection problems in the technical analysis of the financial data. Mathematical Finance – Bachelier Congress 2000, pp. 487–521. Springer, Berlin (2000)
Shiryaev, A., Xu, Z., Zhou, X.: Response to comment on “Thou shalt buy and hold”. Quant. Finance 8, 761–762 (2008a)
Shiryaev, A., Xu, Z., Zhou, X.: Thou shalt buy and hold. Quant. Finance 8, 765–776 (2008b)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Dai, M., Jin, H., Zhong, Y., Zhou, X.Y. (2010). Buy Low and Sell High. In: Chiarella, C., Novikov, A. (eds) Contemporary Quantitative Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03479-4_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-03479-4_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03478-7
Online ISBN: 978-3-642-03479-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)