Optimal Stock Selling Based on the Global Maximum

20 Pages Posted: 23 Feb 2012

See all articles by Min Dai

Min Dai

National University of Singapore (NUS) - Department of Mathematics

Zhou Yang

South China Normal University - Department of Math

Yifei Zhong

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

Date Written: February 22, 2012

Abstract

We aim to determine an optimal stock selling time to minimize the expectation of the square error between the selling price and the global maximum price over a given period. Assuming that stock price follows the geometric Brownian motion, we formulate the problem as an optimal stopping time problem, or equivalently, a variational inequality problem. We provide a partial differential equation (PDE) approach to characterize the resulting free boundary that corresponds to the optimal selling strategy. The monotonicity and smoothness of the free boundary are addressed as well.

Keywords: Optimal selling strategy, global maximum, square error, variational inequality

JEL Classification: Q80 Q35, G60, G40, B91, B28

Suggested Citation

Dai, Min and Yang, Zhou and Zhong, Yifei, Optimal Stock Selling Based on the Global Maximum (February 22, 2012). Available at SSRN: https://ssrn.com/abstract=2009366 or http://dx.doi.org/10.2139/ssrn.2009366

Min Dai (Contact Author)

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

Singapore

Zhou Yang

South China Normal University - Department of Math ( email )

Guangzhou, 510631
China

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

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