Continuous Insider Trading On Dynamic Assets Under Effects Of Partial Observations Or Correlated Noises

Two cases of continuous-time insider trading with a dynamic risky asset value are considered respectively: one is affected by partial observations and the other is affected by a correlated noise between the risky asset value and liquidity trades,and their market equilibrium characteristics and economic significance of the corresponding model are investigated.Firstly,a model of continuous-time insider trading in which the insider is risk-neutral and market makers observe some partial information about the dynamic risky asset is studied.With the help of filtering theory and dynamic programming methods,we establish the existence and uniqueness of the linear Bayesian equilibrium,consisting of insider trading intensity,price pressure on market orders and price pressure on asset observations for trading until a fixed time or for trading until a random time respectively.It shows that when the volatility of observation noise becomes constant,the more information on the asset observed by market makers,the greater price pressure on asset observations is,while the smaller both price pressure on market orders and the insider's profit are.Secondly,a model of continuous-time insider trading in which the insider is risk-averse and market makers possess partial information about the dynamic risky asset is examined.We prove the existence and uniqueness of its linear Bayesian equilibrium under certain conditions.It shows that as time goes by,the insider trading intensity is increasing,but the price pressure on market orders is decreasing while price pressure on asset observations is constant;and price pressure on asset observations decreases as the observation accuracy of partial information decreases but has nothing to do with the risk coefficient of the insider.Finally,a model of continuous-time insider trading in which both the risky asset and liquidity trading volume are affected by a correlated noise is proposed.We prove the uniqueness and existence of the linear Bayesian equilibrium consisting of insider trading strategy and market liquidity.It reveals that if the risky asset is only affected by the correlated noise,then only when the volatility of the risky asset is positively linearly correlated to the volatility of the liquidity trading volume,the insider does not participate in market trading;otherwise,the insider can make positive profit from the transaction.In particular,when both the volatility of the risky asset and the volatility of liquidity trading volume are constant,market liquidity increases as correlated noise volatility increases,while both the trading intensity and expected profit of the insider decrease accordingly.