The self-financing equation in limit order book markets

Rene A. Carmona, Kevin Webster

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


The goal of this paper is to present a mathematical framework for trading on a limit order book, including its associated transaction costs, and to propose continuous-time equations which generalise the self-financing relationships of frictionless markets. These equations naturally differentiate between trading via limit and via market orders, as they include a price impact or adverse selection constraint. We briefly mention several possible applications, including hedging European options with limit orders, to illustrate their impact and how they can be used to the benefit of low-frequency traders. Two appendices include empirical evidence for facts which are not universally recognised in the current literature on the subject.

Original languageEnglish (US)
Pages (from-to)729-759
Number of pages31
JournalFinance and Stochastics
Issue number3
StatePublished - Jul 15 2019

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Finance
  • Statistics, Probability and Uncertainty


  • Limit order book markets
  • Self-financing equation


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