In this paper, we first propose a portfolio management model where the objective is to balance equity and liability. The asset price dynamics includes both permanent and temporary price impact, where the permanent impact is a linear function of the cumulative trading amount and the temporary impact is a kth (between 0 and 1) order power function of the instantaneous trading rate. We construct efficient frontiers to visualize the tradeoff between equity and liability and obtain analytical properties regarding the optimal trading strategies. In the second part, we further consider an optimal deleveraging problem with leverage constraints. It reduces to a non-convex polynomial optimization program with polynomial and box constraints. A Lagrangian method for solving the problem is presented and the quality of the solution is studied. 
Optimal deleveraging with nonlinear temporary price impact