Continuous auctions and insider trading: uniqueness and risk aversion

Abstract

Kyle (1985) and Back (1992) model of continuous-time asset pricing with asymmetric information is studied. A larger class of price processes i s considered, namely price processes that allow the price to depend in a certain nonlinear way on the whole history of the market order. No informed trading (or inconspicuous insider trading) property is proved necessary regardless of how much the informed agent is sensitive to the risk. When the informed agent is risk neutral, it turns out that the price pressure is constant over time and the price depends only on the cumulative market order. As a by product, this paper extends Kyle's and Back's uniqueness result by showing that the equilibrium is also unique on this larger class of price processes. When the informed agent is risk averse, by contrast, the price pressure is strictly decreasing over time and the price depends on the whole history. A unique equilibrium is explicitly constructed. The price pressure in the risk averse case converges uniformly to the price pressure in the risk neutral case, as the informed agent gets less and less risk averse; similarly, the risk averse equilibrium converges to the risk neutral equilibrium.