An optimal control strategy for execution of large stock orders using long short-term memory networks

Andrew Papanicolaou, H. Fu, P. Krishnamurthy, B. Healy, F. Khorrami

Research output: Contribution to journalArticlepeer-review


We simulate the execution of a large stock order with real data and a general power law in the Almgren and Chriss model. The example we consider is the liquidation of a large position executed over the course of a single trading day in a limit order book. Transaction costs are incurred because large orders walk the order book (that is, they consume order book liquidity beyond the best bid/ask price). We model the order book with a power law that is proportional to trading volume, and thus transaction costs are inversely proportional to a power of the trading volume. We obtain a policy approximation by training a long short-term memory (LSTM) neural network to minimize the transaction costs accumulated when execution is carried out as a sequence of smaller suborders. Using historical Standard & Poor’s 100 price and volume data, we evaluate our LSTM strategy relative to strategies based on the time-weighted average price (TWAP) and volume-weighted average price (VWAP). For execution of a single stock, the input to the LSTM is the cross-section of data on all 100 stocks, including prices, volumes, TWAPs and VWAPs. By using this data cross-section, the LSTM should be able to exploit interstock codependence in volume and price movements, thereby reducing transaction costs for the day. Our tests on Standard & Poor’s 100 data demonstrate that in fact this is so, as our LSTM strategy consistently outperforms TWAP-and VWAP-based strategies.

Original languageEnglish (US)
Pages (from-to)37-65
Number of pages29
JournalJournal of Computational Finance
Issue number4
StatePublished - 2023


  • long short-term memory (LSTM) networks
  • optimal execution
  • order books
  • price impact
  • trading volume

ASJC Scopus subject areas

  • Finance
  • Computer Science Applications
  • Applied Mathematics


Dive into the research topics of 'An optimal control strategy for execution of large stock orders using long short-term memory networks'. Together they form a unique fingerprint.

Cite this