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.

中文翻译：

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限价订单簿市场中的自筹资金方程式

本文的目的是提出一个在限价订单簿上进行交易的数学框架，包括其相关的交易成本，并提出连续时间方程，概括无摩擦市场的自筹资金关系。这些方程式自然包括通过限价交易和通过市场订单进行交易，因为它们包括价格影响或逆向选择约束。我们简要地提到了几种可能的应用，包括用限价单对冲欧洲期权，以说明其影响以及如何将其用于低频交易者的利益。两个附录包括事实的经验证据，这些事实在当前关于该主题的文献中并未得到普遍认可。