This paper investigates a financial market where stock returns depend on an unobservable Gaussian mean reverting drift process. Information on the drift is obtained from returns and randomly arriving discrete-time expert opinions. Drift estimates are based on Kalman filter techniques. We study the asymptotic behavior of the filter for high-frequency experts with variances that grow linearly with the arrival intensity. The derived limit theorems state that the information provided by discrete-time expert opinions is asymptotically the same as that from observing a certain diffusion process. These diffusion approximations are extremely helpful for deriving simplified approximate solutions of utility maximization problems.

中文翻译：

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具有高斯漂移的金融市场中随机到达专家意见的扩散近似

本文研究了股票收益取决于不可观察的高斯均值回归漂移过程的金融市场。关于漂移的信息是从回报和随机到达的离散时间专家意见中获得的。漂移估计基于卡尔曼滤波技术。我们研究了高频专家滤波器的渐近行为，其方差随到达强度线性增长。导出的极限定理表明，离散时间专家意见提供的信息与观察某个扩散过程所提供的信息渐近相同。这些扩散近似对于推导效用最大化问题的简化近似解非常有帮助。