Continuous auctions and insider trading: uniqueness and risk aversion

Abstract.

The Kyle (1985) and Back (1992) model of continuous-time asset pricing with asymmetric information is studied. A larger class of price processes is considered, namely price processes that allow the price to depend in a certain way on the path of the market order. A no expected (or inconspicuous insider) trade theorem\/ is satisfied regardless of how much the informed agent is sensitive to the risk. When the informed agent is risk-neutral, the price pressure is constant over time and the price depends only on the cumulative market order. As a corollary, this paper extends Kyle's (1985) and Back's (1992) uniqueness result by showing that the equilibrium is also unique on this larger class of price processes. When the informed agent is risk-averse, in contrast, the price pressure decreases over time and the price depends on the entire path. The price pressure with risk aversion converges uniformly to the risk-neutral price pressure as the informed agent becomes less and less risk-averse; similarly, the equilibrium with risk aversion converges to the risk-neutral equilibrium.