Scott_Pic

We study a continuous time economy where, in addition to an uninformed agent with no private information,  there are insiders who receive private signals throughout time regarding the assets’ terminal payoff. We prove the existence of an equilibrium where, at each private signal time, the public receives a signal of the same form as the associated insider, but of a lower quality.  This causes a jump in both the public information flow, and in the equilibrium asset price.  The resultant market, while complete between each jump, is 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 (whose terminal value X_1 is the risky asset’s terminal payoff), and a continuous time process J taking the form J_t = X_1 + Y_t where Y is an independent Gaussian process.  This coincides with the filtration considered in [Corcuera, Imkeller, Kohatsu-Higa, Nualart 2014 Finance & Stochastics]. 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 entering the market throughout time.