Buy Low and Sell High

16 Pages Posted: 2 Oct 2009

See all articles by Min Dai

Min Dai

National University of Singapore (NUS) - Department of Mathematics

Hanqing Jin

Mathematical Institute; Oxford-Nie Financial Big Data Laboratory; St. Peter's College

Yifei Zhong

University of Oxford - Mathematical Institute; University of Oxford - Mathematical Institute

Xun Yu Zhou

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Date Written: 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 Classification: Q80, Q35, G60, G40, B91, B28

Suggested Citation

Dai, Min and Jin, Hanqing and Zhong, Yifei and Zhou, Xunyu, Buy Low and Sell High (September 1, 2009). Available at SSRN: https://ssrn.com/abstract=1481564 or http://dx.doi.org/10.2139/ssrn.1481564

Min Dai (Contact Author)

National University of Singapore (NUS) - Department of Mathematics ( email )

Singapore

Hanqing Jin

Mathematical Institute ( email )

Andrew Wiles Building
Radicliff Observatory Quarter, Woodstock Road
Oxford, oxfordshire OX2 6GG
United Kingdom

HOME PAGE: http://www.maths.ox.ac.uk

Oxford-Nie Financial Big Data Laboratory ( email )

Andrew Wiles Building
Woodstock Road
Oxford, Oxfordshire OX2 6GG
United Kingdom

St. Peter's College ( email )

New Inn Hall Street
Oxford, Oxfordshire OX1 2DL
United Kingdom

HOME PAGE: http://www.spc.ox.ac.uk

Yifei Zhong

University of Oxford - Mathematical Institute ( email )

Mathematical Institute
24-29 St Giles
Oxford, Oxfordshire OX1 3LB
United Kingdom

University of Oxford - Mathematical Institute ( email )

24-29 St Giles'
Oxford, OX1 3LB
United Kingdom

Xunyu Zhou

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

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