A Markov-driven portfolio execution strategy with market impact

Qingqing Yang, Wai-Ki Ching*, Tak-Kuen Siu, Zhiwen Zhang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


In this paper, we propose a framework for studying optimal agency execution strategies in a Limit Order Book (LOB) under a Markov-modulated market environment. The Almgren-Chriss's market impact model [1] is extended to a more general situation where multiple venues are available for investors to submit trades. Under the assumption of risk-neutrality, a compact recursive formula is derived, using the value iterative method, to calculate the optimal agency execution strategy. The original optimal control problem is then converted to a constrained quadratic optimization problem, which can be solved by using the Quadratic Programming (QP) approach. Numerical examples are given to illustrate the efficiency and effective of our proposed methods.

Original languageEnglish
Pages (from-to)701-728
Number of pages28
JournalNumerical Mathematics
Issue number4
Publication statusPublished - Nov 2018


  • Hamilton-Jacobi-Bellman (HJB) equation
  • Limit Order Book (LOB)
  • Dynamic Programming (DP) principle
  • market impact
  • Quadratic Programming (QP)
  • regime-switching
  • value iteration method


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