Optimal Execution with Quadratic Variation Inventories

Rene Carmona, Laura Leal

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


The first half of the paper is devoted to description and implementation of statistical tests arguing for the presence of a Brownian component in the inventories and wealth processes of individual traders. We use intraday data from the Toronto Stock Exchange to provide empirical evidence of this claim. We work with regularly spaced time intervals, as well as with asynchronously observed data. The tests reveal with high significance the presence of a nonzero Brownian motion component. The second half of the paper is concerned with the analysis of trader behaviors throughout the day. We extend the theoretical analysis of an existing optimal execution model to accommodate the presence of It\^ o inventory processes, and we compare empirically the optimal behavior of traders in such fitted models to the actual behavior we read off the data.

Original languageEnglish (US)
Pages (from-to)751-776
Number of pages26
JournalSIAM Journal on Financial Mathematics
Issue number3
StatePublished - 2023

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Finance
  • Applied Mathematics


  • Brownian motion
  • high-frequency econometrics
  • quadratic variation
  • quantitative finance


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