Optimal execution and price manipulations in limit order book models

Abstract

We analyze the existence of price manipulation and optimal trade execution strategies in a model for an electronic limit order book with nonlinear price impact and exponential resilience. Our main results show that, under general conditions on the shape function of the limit order book, placing deterministic trade sizes at trading dates that are homogeneously spaced is optimal within a large class of adaptive strategies with arbitrary trading dates. Perhaps even more importantly, our analysis yields as a corollary that our model does not admit price manipulation strategies. Last, we will discuss how this result is modified for a constant shape function when the market resilience is no longer exponential.