Short Note on Kyle's Equilibrium Class

The asymmetric information plays critical role in all economics. In the presence of asymmetric information in a given market, market prices of assets are different with those prices under the no arbitrage assumption. It has fundamental effects on the market equilibrium. [1] considered three types of traders: noise trader, informed trader and market maker in a given market in the presence of asymmetric information property. He derived the equilibrium prices of assets. In this short note, Kyle's results are extended. It is seen that a class of equilibrium prices exists, referred as the Kyle's equilibrium class. To this end, first, it is proved that there is a simple linear relation between the variance of equilibrium price and the variance of traded asset size. Then, this simple relation is replaced with a general linear relation. By maximizing the profit function of informed trader, in this case, the Kyle's equilibrium class is derived. Simulation results are also given. Finally, a conclusion section is given.