In a modern financial market, limit order books are usually managed under the price- time priority rule (i.e. orders are ranked by price and then time/position). Empirical studies of limit order books show that the major component of the order flow occurs in the best bid/ask queue [1], and the order’s positional value can be of the same order of magnitude as the bid-ask spread [9]. As a consequence, analyzing the order positions in the best bid/ask queue plays an important role in the field of algorithmic trading.

In this dissertation, we analyze the fluctuation of scaled order positions around their limits in the best bid queue under the general assumption for cancellations, which allows us to generalize the existing result [4, Theorem 15] to include more realistic situations. We first derive the stochastic differential equation that the fluctuation satisfies. Then we prove that the fluctuation is a Gaussian process with mean zero. Furthermore, we show that it has the mean-reverting property, where the mean-reverting level is the same as the fluctuation of scaled best bid queue length multiplied by the order positions relative to the best bid queue length and the mean-reverting speed is proportional to the rate of change of cancellations in the best bid queue.