Multi-agent market equilibria: mathematical models and empirical analyses

Abstract

This thesis examines the framework of multi-agent market equilibria through math- ematical models and empirical analyses. Chapter 2 considers a model for the interaction between a slow institutional investor and a high- frequency trader by means of a stochastic multi-period Stack- elberg game. We determine the unique multi-period Stackelberg equilibrium of the game in terms of the resolvent of a Fredholm integral equation. Our results provide an explicit solution which shows that the high-frequency trader can adopt either predatory or cooperative strategies in each period, depending on the trade-off be- tween the order-flow and the trading signal. We also show that the institutional investor’s strategy is more profitable when the order-flow of the high-frequency trader is taken into account. In Chapter 3 we study a model for a multi-player stochastic differential game, where agents interact through their joint price impact on an asset that they trade to exploit a common trading signal. We prove that a closed-loop Nash equilibrium exists if the price impact parameter is small enough. A comparison with the corre- sponding open-loop Nash equilibrium shows that both the agents’ optimal trading rates and their performance move towards the central-planner solution, since ex- cessive trading due to lack of coordination is reduced. Nevertheless, we find that the size of this effect is modest for plausible parameter values. Chapter 4 develops a methodology which accurately replicates the FTSE Rus- sell indexes reconstruction, including the quarterly rebalancings due to new initial public offerings (IPOs). We apply our index reconstruction protocol to compute the permanent and temporary price impact on the Russell 3000 annual additions and deletions, and on the quarterly additions of new IPOs. Our findings show that the index portfolios following the Russell 3000 index and rebalanced on an annual basis are overall more crowded than those following the index on a quarterly basis.