Heterogeneous Beliefs with Partial Observations

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. * Wilberforce Road, Cambridge CB3 0WB, UK (phone = +44 1223 337969 , email = A.A.Brown@statslab.cam.ac.uk) † I would like to thank Chris Rogers for his suggestion of this avenue of research and for many inciteful comments along the way.