Game-Theoretic Approach for Modeling Market Microstructure

Abstract

This thesis is devoted to investigating possible approaches to endogenous modeling of market microstructure of an auction-based exchange. In chapter II we develop the framework in discrete time and apply it to understanding the economics of trading at high frequency. In chapter III we adapt our modeling approach to continuous time and develop a rich beliefs-driven model of limit-order book evolution between two trades. In the last chapter we introduce discrete admissible prices (i.e. a finite tick size) into our model and investigate the special spatial structures of the equilibria this produces.

Given the novelty of the approach, we have to solve somewhat unusual mathematical problems throughout. We derive a novel estimate of conditional tails of general Ito processes in chapter II, solve a 'non-monotone oblique reflection' RBSDE system and a discontinuous infinite-dimensional fixed point problem in chapter III, and solve a system of control-stopping problems discontinuously coupled through stopping barriers in chapter IV.

We also develop some numerical examples in chapters II and III to illustrate the features of our models and indicate possible applications.