Abstract: In practice,the trader with a large block of shares usually faces endogenous liquidity risk of price impact.So the shares are usually broken up and the trader chooses the optimal strategy to trade.In this paper,the model of price impactis expanded.Supposing price impact with stochastic and nonlinear,we established the model of the stochastic and nonlinear price impact.The results show that the trader liquidation speed is obviously confined and the speed is constant under stochastic and quadratic price impact function.The parameters sensitivity of optimal strategy is also analyzed in the paper:in early days,the greater σ and α are,the greater liquidation speed is.The liquidation position reduction is more close to linear with γ、β and θ increasing.We also highlight that the optimal liquidation time should be investigated under internal and external conditions.

Key words: stochastic, nonlinear, optimal liquidation