Equilibrium of Insider Trading on Dynamic Asset with Stochastic Liquidity under Partial Observations

A general model of insider trading on a dynamic asset in a finite time interval is proposed, in which an insider possesses the whole information on the dynamic values, noise traders without any information submit orders randomly as a martingale with volatility following a stochastic process, and market makers observe partial information when setting price in a semi-strong efficient way. With the help of filtering theory, BSDE method and dynamic programming principle, we establish a market equilibrium consisting of linear insider trading strategy and linear pricing rule, with the later characterized by price pressure on market orders and price pressure on asset observations. It shows that in the equilibrium, all the information on the risky asset is incorporated into the market price at the end of the transaction, and price pressure on market orders is a submartingale while market depth process is a martingale. Furthermore, as market makers’ information precision on the asset tends to zero, the equilibrium with partial observation of market makers on the risky asset converges to the one without partial observation of market makers, while when market makers observe almost all of information on the asset, the expected profit earned by the insider makes almost zero, which is in accord with our economic intuition. Our results cover some classical results about continuous-time insider trading on a static asset.