英文标题：
《Exact and asymptotic solutions of the call auction problem》
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作者：
Ioane Muni Toke
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最新提交年份：
2014
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英文摘要：
  The call auction is a widely used trading mechanism, especially during the opening and closing periods of financial markets. In this paper, we study a standard call auction problem where orders are submitted according to Poisson processes, with random prices distributed according to a general distribution, and may be cancelled at any time. We compute the analytical expressions of the distributions of the traded volume, of the lower and upper bounds of the clearing prices, and of the price range of these possible clearing prices of the call auction. Using results from the theory of order statistics and a theorem on the limit of sequences of random variables with independent random indices, we derive the weak limits of all these distributions. In this setting, traded volume and bounds of the clearing prices are found to be asymptotically normal, while the clearing price range is asymptotically exponential. All the parameters of these distributions are explicitly derived as functions of the parameters of the incoming orders\' flows.
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中文摘要：
集合竞价是一种广泛使用的交易机制，尤其是在金融市场的开盘和收盘期间。在本文中，我们研究了一个标准的集合拍卖问题，其中订单按照泊松过程提交，随机价格按照一般分布分布，并且可以随时取消。我们计算了集合竞价的交易量分布、清算价格的上下限以及这些可能清算价格的价格范围的解析表达式。利用序统计理论的结果和具有独立随机指数的随机变量序列的极限定理，我们导出了所有这些分布的弱极限。在这种情况下，交易量和清算价格的界限是渐近正态的，而清算价格的范围是渐近指数的。这些分布的所有参数都显式地导出为传入订单流参数的函数。
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分类信息：

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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一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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