Equilibrium with Insider Information
Department of Applied Mathematics
Questrom School of Business, Boston University
In this talk, we will discuss the role of inside information in determining asset prices. Specifically, we consider when, in a competitive economy, an insider receives an initial signal about the terminal value of a traded asset ("stock"). As the insider will alter her trading based upon this signal, it is of interest to know precisely what information is being passed along to the market, and what are the effects on prices and optimal share demands. After presenting the static case with exponential preferences and Gaussian payoffs/signals, (introduced in a series of papers by Sanford Grossman, Martin Hellwig and Joseph Stiglitz the 1970s and 1980s), we will extend analysis both to continuous time, and beyond Gaussian payoffs. In both the static and dynamic settings, the key problem is to identify how the terminal stock distribution changes, conditional upon the insider and market signals, and then to use this to ascertain the specific form of the market signal. In particular, in continuous time there are multiple filtration enlargements, and very delicate issues surrounding arbitrage, measurability, and endogenous market completeness. Time permitting, we will discuss what happens when, instead of a single initial signal, there is a flow of signals occurring throughout time.
This is joint work with Jerome Detemple and Marcel Rindisbacher of Boston University.