Asymptotic Analysis For Mixed Strategy Equilibrium Of Two Insiders’ Trading In High Frequency Trading Case

By the model in Gong and Zhou (2010) as the prototype, we expand the study of the insider trading problem. The model assumes the existence of a risk asset markets, and there is a risk asset in the market. Traders on the risky assets involved in the transaction are divided into three categories. The first is insider traders, having private information, choose the optimal trading strategy to maximize its own revenue target selection, and the model assumes that the number of inside traders is two, The Second is noise traders, who are without any private information, and in fact provide cover for inside traders. The third is a market maker, formulated the rational expectations price, according to the total trading volume which is number of the inside traders’and noise traders’filers, as well as the public history information,.The two assumptions on equilibrium definition are:1.Inside traders maximize their profits, in other word, in each of the transaction inside traders choose the optimal trading volume to maximize their related parts of expected future total profit, according to their risk attribute, private information and historical information;2. Market conditions of validity:the price sequence is a martingale with respect to the information flow generated by sequence of total trading volume.The following three models are studied:1. two inside traders are risk preference, priority to maximize the risk-profit, and then maximize the security-profit;2. two inside traders are risk neutral, maximize the expected future total profit in advance;3. two inside traders are risk aversion, firstly maximize the security-profit, and then maximize the risk-profit.We mainly consider mixed strategy equilibrium of the three types of inside traders’ trading in the high frequency trading case. The high-frequency trading refers to that, in time interval [0,1], there are a lot of transactions by traders, and time period between two near transactions is very short. When the transaction number tends to infinity, the direct limits of the economic and financial variables are extraordinary, since those limits are zero or infinity. Hence, we need to do asymptotic analysis on the mixed strategy equilibrium for three types of insider trading in the high frequency trading case. We not only calculate the speed of the variables tends to zero or infinity, but also obtain limits of the normalized variables which are the variables divided their speeds of tends to zero or infinity, so get the nontrivial continuous solutions.The main results are as follows:the speeds and limits of the normalized variables about trading intensity, the remaining amount of information and market liquidity parameter, comparative analysis with models in Gong and Zhou (2010) that there is only an inside trader on the market, and the impact of trading intensity, the remaining amount of information and market liquidity parameter with respect to the number of insider trading and risk attribute.