The Existence Of Linear Strategy Of Insider Trading In Continuous Time

In this paper, we study insider trading in continuous time. In a risk asset market, its liquidation value in continuous time meets a dynamic equation dVt= σtvdBtv,where the initial value V0 is normal distributed as N(vo, so), Btv is Standard Brownian motion inde-pendent of V0, and σtv is a deterministic continuous differentiable functions with respect to time t in [0, T]. There are three different types of traders in the market:one is insider who process the reality of liquidation value; the second type of noise traders, do have no information about the liquidation value; Third class consists of market makers, according to total trading volume of the insider and noise traders and the probability distribution of liquidation value at each time, who give a price of the liquidation value. In this way, the insider can make use of his private information to obtain profits under the guise of noise traders. In this paper, by using the method of filtering theory, we find the optimal strategy of insider trading. Moreover we discuss the existence of Cournot equilibrium between two insiders. Full text is divided into five chapters.The first chapter is the introduction. The second chapter for prepare knowledge, mainly applied in this paper, gives an introduce of Brownian motion and filtering theorem. In the third chapter, we give an insider trading model in continuous time and solve the optimal linear strategy by the use of filtering theory. And in Chapter 4, the existence of Cournot equilibrium between two insiders are also discussed, which includes the non-existence result of Zhou (2015). The fifth chapter gives the summary and outlook for this article.