Alberto Bressan, Dissertation Advisor/Co-Advisor Alberto Bressan, Committee Chair/Co-Chair Francesca Chiaromonte, Committee Member Lyle Norman Long, Committee Member Anna L Mazzucato, Committee Member Victor Nistor, Committee Member Yuxi Zheng, Committee Member Constantino Manuel Lagoa, Special Member
Keywords:
Limit Order Book Mathematical Finance Measure Valued Optimization Nash equilibrium Optimal Control Price Impact.
Abstract:
We introduce a new model of the Limit Order Book, viewed as a noncooperative game, whose players are the agents submitting the Limit Orders. The incoming Market Order is modeled as a random variable.
If we allow prices to range in a compact interval, we can prove the existence or non-existence of Nash equilibria in the case of homogeneous players. When a Nash equilibrium exists, we prove that it is unique, and obtain explicit formulas for the optimal bidding strategies, by solving a system of Ordinary Differential Equations.
If prices take values in a finite set, we show the existence or non-existence of a Nash equilibrium in the more general case of heterogeneous players.
