题目：Quantitative Investment: From low-medium frequency trading to high frequency trading
郑坂，博士，法国领先资产管理公司（法国兴业银行集团）研究员。巴黎综合理工大学(École Polytechnique)和法国国立统计与经济管理学院(ENSAE ParisTech)工程师，法国国立高等电信学院(Télécom ParisTech)应用数学专业博士。从事资产管理领域的研究工作，专注于金融大数据的处理，对冲基金的投资策略，指数跟踪产品的研究以及量化管理基金的策略开发。现兼任同济大学法国校友会会长及法国博效基金会秘书长。
We provide a review on quantitative methods for low-medium frequency trading and high frequency trading. For low-medium frequency trading, we review the different econometric estimators to extract a trend of a time series which is widely used in momentum strategies. We distinguish between linear and nonlinear models as well as univariate and multivariate filtering. For high frequency trading, we introduce a multivariate point process describing the dynamics of the Bid and Ask price of a financial asset. The point process is similar to a Hawkes process, with additional constraints on its intensity corresponding to the natural ordering of the best Bid and Ask prices. We study this process in the special case where the fertility function is exponential so that the process is entirely described by an underlying Markov chain including the constraint variable. Natural, explicit conditions on the parameters are established that ensure the ergodicity of the chain. Moreover, scaling limits are derived for the integrated point process.
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