abstract: "Optimal execution and trading algorithms rely on price impact models, such as the propagator model, to quantify the cost of trading. 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. However, we show that in the scaling limit of small and frequent orders, the nonlinear model can be approximated by a linear model, where a stochastic liquidity parameter proxies the nonlinearity of the original impact function. This allows us to extend results for absence of price manipulation, optimal trading, and mean-field games to concave models. We also illustrate the practical usefulness of the approximation using LOBSTER limit-order data.
(Joint work in progress with Kevin Webster and Zexin Wang.)"