英文标题：
《Low-traffic limit and first-passage times for a simple model of the
continuous double auction》
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作者：
Enrico Scalas, Fabio Rapallo, Tijana Radivojevi\\\'c
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最新提交年份：
2016
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英文摘要：
We consider a simplified model of the continuous double auction where prices are integers varying from $1$ to $N$ with limit orders and market orders, but quantity per order limited to a single share. For this model, the order process is equivalent to two $M/M/1$ queues. We study the behaviour of the auction in the low-traffic limit where limit orders are immediately transformed into market orders. In this limit, the distribution of prices can be computed exactly and gives a reasonable approximation of the price distribution when the ratio between the rate of order arrivals and the rate of order executions is below $1/2$. This is further confirmed by the analysis of the first passage time in $1$ or $N$.
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中文摘要：
我们考虑一个简化的连续双重拍卖模型，其中价格为整数，从1美元到N美元不等，有限价订单和市场订单，但每份订单的数量仅限于一股。对于该模型，订单流程相当于两个$M/M/1$队列。我们研究了低流量限制下的拍卖行为，在这种情况下，限价指令会立即转化为市场指令。在这个极限下，当订单到达率和订单执行率之间的比率低于1/2美元时，可以准确计算价格分布，并给出价格分布的合理近似值。这一点通过对1美元或N美元首次通过时间的分析得到进一步证实。
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分类信息：

一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Quantitative Finance 数量金融学
二级分类：Trading and Market Microstructure 交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
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