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Dynamic trading strategies with stochastic and nonlinear price impact

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 will choose the optimal strategy to trade. In this paper, the model of price impact is 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 in almost whole time under stochastic quadratic price impact function. The parameters sensitivity of optimal strategy is also analyzed in the dissertation: in early days, the greater sigma and alpha are, the greater liquidation speed is. The liquidation position reduction is more close to linear with gamma, beta and thetas increasing. We also highlight that the optimal liquidation time should be investigated on internal and external conditions.