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The continuous-time version of Kyle’s (1985) model of asset pricing with asymmetric information is studied. It is shown that there is a unique equilibrium pricing rule within a certain class. This pricing rule is obtained in closed form for general distributions of the asset value. A particular example is a lognormal distribution, for which the equilibrium price process is a geometric Brownian motion. General trading strategies are allowed. In equilibrium, the informed agent, who is risk neutral, has many optima, but he does not correlate his trades locally with the noise trades nor does he submit discrete orders.
Kerry Back (Wed,) studied this question.