Nonlinear price impact and portfolio choice

In a market with price impact proportional to a power of the order flow, we find optimal trading policies and their implied performance for long-term investors who have constant relative risk aversion and trade a safe asset and a risky asset following geometric Brownian motion. These quantities admit asymptotic explicit formulas up to a structural constant that depends only on the curvature of the price impact function. Trading rates are finite as with linear impact, but are lower near the target portfolio, and higher away from the target. The model nests the square-root impact law and, as extreme cases, linear impact and proportional transaction costs.