Heterogeneous Beliefs with Partial Observations

TL;DR

This paper models a financial market with agents holding heterogeneous beliefs about an unobserved process, using filtering techniques to derive asset prices and interest rates based on partial observations of dividends.

Contribution

It introduces a novel framework combining heterogeneous beliefs and filtering to analyze asset pricing with partial information.

Findings

Derived the state price density and riskless rate.

Characterized risky asset prices via differential equations.

Analyzed the impact of belief heterogeneity on asset prices.

Abstract

This paper examines a heterogeneous beliefs model in which there is a process that is only partially observed by the agents. The economy contains a risky asset producing dividends continuously in time. The dividends are observed by the agents. The dividends are assumed to be a known function of some other unobserved process. The agents use filtering to estimate the value of this unobserved process. The agents have different beliefs about the dynamics of the unobserved process and therefore form different estimates. We analyse this model and derive the state price density. We use this to derive the riskless rate. We also characterise the price of the risky asset in terms of the solution of a series of differential equations.