Stochastic Liquidity as a Proxy for Nonlinear Price Impact
证明在订单小而频繁的扩散极限下，非线性价格冲击模型收敛为易处理的线性模型，随机流动性参数可近似原始冲击函数的非线性，从而推导出最优交易策略的简单公式及排除价格操纵的市场容量条件，并用高频限价订单数据验证了理论结果。
For the “In This Issue” column: Trading costs play a central role in designing and implementing quantitative trading strategies. To quantify trading costs, optimal execution and trading algorithms rely on price impact models, such as the propagator model. Empirically, price impact is concave in trade sizes, leading to nonlinear models for which optimization problems are intractable and even qualitative properties, such as price manipulation, are poorly understood. This paper shows that, in the diffusion limit of small and frequent orders, the nonlinear model converges to a tractable linear model. In this high-frequency limit, a stochastic liquidity parameter approximates the original impact function’s nonlinearity. This allows us to derive simple formulas for optimal trading strategies and sharp conditions on market volumes to rule out price manipulation. A detailed empirical study using high-frequency limit-order data illustrates the practical performance of the theoretical results.