# Asymptotic Filter Behavior for High-Frequency Expert Opinions in a Market with Gaussian Drift

## TL;DR

This paper analyzes how high-frequency expert opinions influence the estimation of a hidden Gaussian drift in a financial market, showing that increased opinion arrival rates lead to full information about the drift.

## Contribution

It demonstrates the asymptotic behavior of the Kalman filter in a market with noisy expert opinions, proving convergence to full information as opinion frequency increases.

## Key findings

- Conditional mean converges to the true drift
- Estimation becomes consistent with high-frequency opinions
- Filter asymptotics show full information in the limit

## 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.