Equilibrium execution strategies with generalized price impacts (Financial Modeling and Analysis)

Abstract

This paper examines the execution problem of large traders with generalized price impact model. Constructing a model in a discrete-time setting, we solve this problem by applying the backward induction method of the dynamic programming. In this model, we formulate the expected utility maximization problem of multiple large traders as a Markov game and derive an equilibrium execution strategy at a Markov perfect equilibrium. This model enables us to investigate how the execution strategies and trade performances of these large traders are affected by the existence of other traders. Moreover, we find that these equilibrium execution strategies become deterministic when the total execution volumes of non large traders are deterministic. We also show, by some numerical examples, the comparative statics results with respect to several problem parameters.