Insider Trading When The Information Is Incomplete

In this thesis , we extend the Gong and Zhou’s dynamic model by assuming thatthe insider’s information is partial. The insider may only obtain a noisy version of thefuture value rather than the insider knows exactly the future value of the asset.According to the characteristic of the conditional expectation of the informed profits,three different models vary with insider’s attitudes regarding to risk are presented.They are risk-aversion insider’s model, risk-neutral insider’s model and risk-seekinginsider’s model. Frist of all , we give the discrete equilibrium of the three models. andthen , according to the discrete equilibrium, we acquired the continuous equilibriumof those models.In this paper , three kinds of traders are involved. They are insider, noise traderand market marker. The marker maker who owns the observation of the total order ofinsider and noise trader combined.The market marker based on all his information available at the moment to make abest evaluation for the liquidity price. pn= E(νy1 ,L,yn)( according to the marketefficiency ). The marker maker absorbs all the orders to keeping the market liquidityand the public investment requirements. The insider , the one has private informationand make profit by his private information. To maximize his future profit he choosehis optimal trading strategies conditional on his private information as well ashistorical public information. The noise insider has no information about the assetand doesn’t willing to spend money and time to get the information of the asset. Theaim of the noise insider is to get money immediately.This paper has two assumptions , as follows :1,The Profit Maximization 2,TheMarket Efficiency. We get the linear equilibrium endogenously by using the methodof orthogonalization and the Asymptotic Analysis. We use the method oforthogonalization getting those . the orthogonalizationof {y1 ,L,yn,}produces{~y1 ,L,~yn}which is the zero average Gaussian random variable. From this we cangetpn=pn 1+λn~ynandσ(y1,L,yn,ν+ε)=σ(~y1,L,~yn,ν~n(ε)),the next answerscan be solved by this. In the process of seeking continuous result ,we imposemethod’s Asymptotic Analysis. This avoid the trivial results in limit ,insteadnon-trivial results can be obtained definitely by the concept of“convergence speed” which is more useful .At last, we give the economic significance of the three models. On one hand , theunreleased information is decreasing to little when trading opportunities is going toinfinity. The insider’s trading is more cautious when his information is moreincomplete. On the other, the information of asset’s real valve can’t release to zeroand the insider’s information is more incomplete and more information not release.