作为市场非均衡度量的最优交易策略
Optimal Trading Strategies as Measures of Market Disequilibrium
摘要：
对于高频交易数量的分类，等待时间，会话内和会话之间的价格增量被称为a-，b-和c-增量。a-b-c增量的统计是针对芝加哥商品交易所集团为Globex上交易的期货发布的时间和销售记录计算的。Weibull分布、Kumaraswamy分布、Riemann分布和Hurwitz Zeta分布、抛物线分布、Zipf-Mandelbrot分布均对a增量和b增量进行了检验。一个离散版本的Fisher-Tippett分布的建议近似的极端b-增量。回顾了与期货价格限制相关的随机、典型和混沌随机序列的Kolmogorov和Uspenskii分类。应用非参数L1和对数似然检验来检查a增量和b增量之间的依赖性。最大利润策略和最优交易要素被建议作为市场报价和非均衡的频率和幅度的度量。最优利润的经验累积分布函数的报告。通过对一些经典文献的详细回顾，追溯现代金融学的起源和基础。
英文摘要：
For classification of the high frequency trading quantities, waiting times, price increments within and between sessions are referred to as the a-, b-, and c-increments. Statistics of the a-b-c-increments are computed for the Time & Sales records posted by the Chicago Mercantile Exchange Group for the futures traded on Globex. The Weibull, Kumaraswamy, Riemann and Hurwitz Zeta, parabolic, Zipf-Mandelbrot distributions are tested for the a- and b-increments. A discrete version of the Fisher-Tippett distribution is suggested for approximating the extreme b-increments. Kolmogorov and Uspenskii classification of stochastic, typical, and chaotic random sequences is reviewed with regard to the futures price limits. Non-parametric L1 and log-likelihood tests are applied to check dependencies between the a- and b-increments. The maximum profit strategies and optimal trading elements are suggested as measures of frequency and magnitude of the market offers and disequilibrium. Empirical cumulative distribution functions of optimal profits are reported. A few classical papers are reviewed with more details in order to trace the origin and foundation of modern finance.
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