英文标题：
《Brownian trading excursions and avalanches》
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作者：
Friedrich Hubalek and Paul Kr\\\"uhner and Thorsten Rheinl\\\"ander
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最新提交年份：
2017
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英文摘要：
We study a parsimonious but non-trivial model of the latent limit order book where orders get placed with a fixed displacement from a center price process, i.e.\\ some process in-between best bid and best ask, and get executed whenever this center price reaches their level. This mechanism corresponds to the fundamental solution of the stochastic heat equation with multiplicative noise for the relative order volume distribution. We classify various types of trades, and introduce the trading excursion process which is a Poisson point process. This allows to derive the Laplace transforms of the times to various trading events under the corresponding intensity measure. As a main application, we study the distribution of order avalanches, i.e.\\ a series of order executions not interrupted by more than an $\\varepsilon$-time interval, which moreover generalizes recent results about Parisian options.
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中文摘要：
我们研究了一个简约但非平凡的潜在限制订单簿模型，其中订单是以中心价格过程的固定位移下达的，即介于最佳出价和最佳询问之间的某个过程，并且在该中心价格达到其水平时执行。这种机制对应于相对有序体积分布的带乘性噪声的随机热方程的基本解。我们对各种类型的交易进行了分类，并介绍了交易漂移过程，即泊松点过程。这允许导出相应强度度量下不同交易事件的时间拉普拉斯变换。作为一个主要应用，我们研究了订单雪崩的分布，即一系列订单执行没有被超过$\\ varepsilon$-时间间隔中断，这进一步推广了关于巴黎期权的最新结果。
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分类信息：

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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