The Sound of Silence: equilibrium filtering and optimal censoring in financial markets

Abstract: Following the approach of standard filtering theory, we analyse investor-valuation of firms, when these are modelled as geometric-Brownian state processes that are privately and partially observed, at random (Poisson) times, by agents. Tasked with disclosing forecast values, agents are able purposefully to withhold their observations; explicit filtering formulas are derived for downgrading the valuations in the absence of disclosures. The analysis is conducted for both a solitary firm and m co-dependent firms.