Nash Equilibrium Of Information Protocol In Continuous-time Insider Trading With Perfect Information

In a financial market,there is a model of continuous-time insider trading in perfect competition,where under the cover of noise traders,multiple insiders have perfect information about the value of risky assets to choose trading strategies to maximize their profits in a semi-efficient pricing way.Back,Cao and Willard(2000)proved that there is not a linear equilibrium in the market with at least two insiders;and Zhou(2016)independently proved that there is not a linear Cournot equilibrium in the market with two insiders.In view of the above,this thesis continues to study the existence of market equilibrium in perfect competition for such continuous-time insider trading model,with two aspects in the following:On the one hand,aiming at the model of Stackelberg game of continuoustime insider trading for two insiders with perfect information,with the help of filtering theory,dynamic programming principle and variational principle,it is proved that the leader do not participate in the trading all the time,that is,there is no linear market equilibrium in this model.This may be due to the fact that the follower possesses fully the information on the underlying risky asset and can track constantly the trading information of the leader,thereby monopolize the entire market,leading to a lack of profitability and motivation for the leader to participate in the trading.This is in sharp contrast to the result of the first mover advantage in the classic Stackelberg product competition.On the other hand,for the model of n-insider trading symmetric game in continuous-time perfect competition,a concept of Nash equilibrium of information protocol under semi-strong efficient pricing is proposed.By the use of filtering theory and maximum principle,the characteristics and numerical simulation analysis of all Nash equilibria of prior information protocol are obtained.It shows that in a market with at least two insiders,each Nash equilibrium of prior information protocol requires each insider to release only partial but not all private information when everyone selects optimal strategy to obtain positive profit;in a market with a single insider,she/he must release all private information to achieve maximum profit.Finally,using backward induction method,we prove that there exists a unique Nash equilibrium of information protocol in the market with any number of insiders,in which market makers always set a local linear price at any time based on the total cumulative market order in the market.This provides a theoretical basis for insiders to make optimal decisions and for market makers to set pricing effectively.Our research results,especially the proposed concept of Nash equilibrium of information protocol,provide new ideas for multiple insiders with perfect information in continuous-time insider trading to win positive profit.