Optimal portfolio execution with a Markov chain approximation approach

Jingnan Chen, Liming Feng, Jiming Peng, Yu Zhang

Research output: Contribution to journalArticlepeer-review

Abstract

We study the problem of executing a large multi-asset portfolio in a short time period where the objective is to find an optimal trading strategy that minimizes both the trading cost and the trading risk measured by quadratic variation. We contribute to the existing literature by considering a multi-dimensional geometric Brownian motion model for asset prices and proposing an efficient Markov chain approximation (MCA) approach to obtain the optimal trading trajectory. The MCA approach allows us not only to numerically compute the optimal strategy but also to theoretically analyse the influence of factors such as price impact, risk aversion and initial asset price on the optimal strategy, providing both quantitative and qualitative guidance on the trading behaviour. Numerical results verify the theoretical conclusions in the paper. They further illustrate the effects of cross impact and correlations on the optimal execution strategy in a multi-asset liquidation problem.

Original languageEnglish (US)
Pages (from-to)165-186
Number of pages22
JournalIMA Journal of Management Mathematics
Volume34
Issue number1
DOIs
StatePublished - Jan 1 2023

Keywords

  • Markov chain approximation
  • cross-asset price impact
  • linear extrapolation
  • multi-dimensional binomial method
  • portfolio execution

ASJC Scopus subject areas

  • Management Information Systems
  • Modeling and Simulation
  • Economics, Econometrics and Finance(all)
  • Strategy and Management
  • Management Science and Operations Research
  • Applied Mathematics

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