A Class of Optimal Liquidation Problem with a Nonlinear Temporary Market Impact

We extend the self-exciting model by assuming that the temporary market impact is nonlinear and the coefficient of the temporary market impact is an exponential function. Through optimal control method, the optimal strategy satisfies the second-order nonlinear ordinary differential equation. The specific form of the optimal strategy is given, and the decreasing property of the optimal strategy is proved. A numerical example is given to illustrate the financial implications of the model parameter changes. We find that the optimal strategy of a risk-neutral investor changes with time and investment environment.