The Equilibrium In Continuous Insider Trading Under The Pricing Of Partial Observations

In this paper,we mainly study a class of insider trading in which market makers could observe partial information on a risky asset in continuous time,and we investigate the existence of the equilibrium consisting of an optimal linear strategy and the semi-strong efficiency pricing rule.Firstly,we study insider trading in continuous time in which an insider possesses long-lived information on a risky asset and market makers observe the total traded volume in the market and some distorted or overconfident signals of the risky asset.By applying the Kalman-Bucy filtering theory,we prove that there exists an unique optimal linear insider trading strategy under the semi-strong efficiency pricing rule,and find that the information possessed by the insider is all released in the trading end and that the insider trading intensities increase with the the increasing of the degree of the amplified distortion(kei1..?)and the overconfident degree of the signal of the risky asset observed by market makers,but the corresponding profits of the insider decrease;also we find that the insider trading intensities decrease with the the increasing of the degree of the shrink distortion(kei1..?)of the risky asset observed by market makers,but the corresponding profits of the insider increase.Secondly,we study a class of continuous insider trading when the risk asset is dynamic and market makers observe not only the total traded volume,but also some noisy signals on a risky asset.We get a closed form of optimal linear strategy of the continuous insider trading under the semi-strong efficiency pricing rule.And we find that the more accurate the information on the value of the risk asset observed by the market makers,the pricing rule of the risk asset is closer to its real pricing rule,and the less the positive profits are made by the informed trader.