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.

中文翻译：

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非线性价格影响和投资组合选择

在价格影响与定单流量成正比的市场中，我们发现了长期交易者的最佳交易策略及其隐含的表现，这些长期投资者具有相对的相对风险厌恶感，并按照几何布朗运动来交易安全资产和风险资产。这些数量允许渐进式显式公式，直到结构常数仅取决于价格影响函数的曲率。与线性影响一样，交易汇率是有限的，但在目标投资组合附近较低，而在目标组合附近则较高。该模型嵌套平方根影响定律，在极端情况下，嵌套线性影响和比例交易成本。