Incomplete and Asymmetric Information in Asset Pricing Theory

These notes could equally well be entitled “Applications of Filtering in Financial Theory.” They constitute a selective survey of incomplete and asymmetric information models. The study of asymmetric information, which emphasizes differences in information, means that we will be concerned with equilibrium theory and how the less informed agents learn in equilibrium from the more informed agents. The study of incomplete information is also most interesting in the context of economic equilibrium.Excellent surveys of incomplete information models in finance [48] and of asymmetric information models [10] have recently been published. In these notes, I will not attempt to repeat these comprehensive surveys but instead will give a more selective review.The first part of this article provides a review of filtering theory, in particular establishing the notation to be used in the later parts. The second part reviews some work on incomplete information models, focusing on recent work using simple Markov chain models to model the behavior of the market portfolio. The last part reviews asymmetric information models, focusing on the Kyle model and extensions thereof.