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In general, optimal trade execution is considered the problem of finding a strategy that executes a trade of a certain volume of an asset within a defined time period at a minimal cost (Bertsimas Lo, 1998; Chen et al., 2018).
A limit order book trading strategy is a method of trading that involves tracking and analyzing the order book of a given market. It involves placing orders based on the current market conditions, as well as using the order book to predict future price movements.
The fill probability, or execution probability, refers to the likelihood that a limit order is executed. This probability is affected by both intrinsic characteristics of an order, such as the price and quantity, and by external factors, mainly determined by the market conditions at the time the order is submitted.
Limit Order Book Explained Traders execute limit orders to buy or sell securities at a specified price or better. A buy limit order entails purchasing assets at a certain value or less, while a sell order limit means selling at a minimum price given or more.
The form of the optimal execution strategy is to make an initial lump purchase and then purchase continuously for some period of time during which the rate of purchase is set to match the order book resiliency.
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It is a transparent system that matches customer orders (e.g. bids and offers) on a price time priority basis. The highest (best) bid order and the lowest (cheapest) offer order constitutes the best market or the touch in a given security or swap contract.

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