Optimal stock selling based on the global maximum

Min Dai, Zhou Yang, Yifei Zhong

Research output: Journal article publicationJournal articleAcademic researchpeer-review

5 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1804-1822
Number of pages19
JournalSIAM Journal on Control and Optimization
Issue number4
Publication statusPublished - Aug 2012


  • Global maximum
  • Optimal selling strategy
  • Square error
  • Variational inequality

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics


Dive into the research topics of 'Optimal stock selling based on the global maximum'. Together they form a unique fingerprint.

Cite this