Non-linearity of Market Impact Functions : Empirical and Simulation-based Studies on Convex/Concave Market Impact Functions and Derivation of an Optimal Execution Model(Application,<Special Topics>Activity Group "Mathematical Finance")

Abstract

Market impact is one of the typical liquidity problems in financial markets. In this paper, we focus on convexity/concavity of market impact functions. We treat some simple empirical study and simulation-based study to investigate the forms of market impact functions which are consistent with the real market. Moreover, we derive a theoretical model of optimal execution problem with general-shape market impact functions and study mathematical properties of corresponding value functions.