Equilibrium with Heterogeneous Information Flows

We study a continuous time economy where throughout time, insiders receive private signals regarding the risky assets' terminal payoff. We prove existence of a partial communication equilibrium where, at each private signal time, the public receives a signal of the same form as the associated insider, but of lower quality. This causes a jump in both the public information flow and equilibrium asset price. The resultant markets, while complete between each jump time, are incomplete over each jump. After establishing equilibrium for a finite number of private signal times, we consider the limit as the private signals become more and more frequent. Under appropriate scaling we prove convergence of the public filtration to the natural filtration generated by both the fundamental factor process $X$ and a continuous time process $J$ taking the form $J_t = X_1 + Y_t$ where $X_1$ is the terminal payoff and $Y$ an independent Gaussian process. This coincides with the filtration considered in 'Additional Utility of Insiders with Imperfect Dynamical Information' (Corcuera, et al. Finance & Stochastics 2004). However, while therein the filtration was exogenously assumed to be that of an insider who observes a private signal flow, here it arises endogenously as the public filtration when there are a large number of insiders receiving signals throughout time.