Abstract This paper investigates a financial market where stock returns depend on a hidden Gaussian mean reverting drift process. Information on the drift is obtained from returns and expert opinions in the form of noisy signals about the current state of the drift arriving at the jump times of a homogeneous Poisson process. Drift estimates are based on Kalman filter techniques and described by the conditional mean and covariance matrix of the drift given the observations. We study the filter asymptotics for increasing arrival intensity of expert opinions and prove that the conditional mean is a consistent drift estimator; it converges in the mean-square sense to the hidden drift. Thus, in the limit as the arrival intensity goes to infinity investors have full information about the drift.

中文翻译：

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具有高斯漂移的市场中高频专家意见的渐近滤波器行为

摘要 本文研究了一个金融市场，其中股票收益取决于隐藏的高斯均值回归漂移过程。关于漂移的信息是从有关漂移的当前状态的噪声信号形式的回报和专家意见中获得的，这些信号到达齐次泊松过程的跳跃时间。漂移估计基于卡尔曼滤波器技术，并由给定观测值的漂移的条件均值和协方差矩阵描述。我们研究了用于增加专家意见到达强度的滤波器渐近性，并证明条件均值是一致的漂移估计量；它在均方意义上收敛到隐藏漂移。因此，当到达强度达到无穷大时，投资者拥有关于漂移的完整信息。