Ap- plication of the cluster expansion to a mathematical model of the long memory phenomenon in a financial market
Ap- plication of the cluster expansion to a mathematical model of the long memory phenomenon in a financial market
复制标题
集群扩展在金融市场长记忆现象数学模型中的应用
DOI：
10.1007/s10955-013-0783-z
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发表时间：
2013
影响因子：
1.6
通讯作者：
J. Murai
中科院分区：
文献类型：
--
作者：
K. Kuroda;J.Maskawa;J. Murai
对股票市场高频数据的实证研究表明，交易符号或交易卷的时间序列具有长记忆性。本文给出了描述交易者交易策略的聚合物模型的离散时间随机过程，并证明了该过程的尺度极限收敛于具有Hurst指数和布朗运动的分数阶布朗运动的叠加，前提是交易者投资策略的时间尺度指数γ与离散时间过程中相互作用范围的指数δ一致。研究的主要工具是统计力学数学研究中发展起来的簇展开方法。
Empirical studies of the high frequency data in stock markets show that the time series of trade signs or signed volumes has a long memory property.In this paper, we present a discrete time stochastic process for polymer model which describes trader’s trading strategy, and show that a scale limit of the process converges to superposition of fractional Brownian motions with Hurst exponentsand Brownian motion, provided that the indexγof the time scale about the trader’s investment strategy coincides with the indexδof the interaction range in the discrete time process. The main tool for the investigation is the method of cluster expansion developed in the mathematical study of statistical mechanics.