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Probability and Computational Finance Seminar
Sergey Nadtochiy
University of Michigan
Title: Control-Stopping Games for Market Microstructure

Abstract: In this talk, I present a framework for modeling market microstructure based on continuous-time control-stopping games. In this framework, the shape and dynamics of a Limit Order Book (LOB) arise as an outcome of an equilibrium between multiple agents who have different believes about the future demand for an asset. These beliefs may change according to the information observed by the agents (e.g. represented by a relevant stochastic factor), implying a change in the shape of the LOB. The proposed framework allows one to see how changes in the relevant information signal affect the LOB. In addition, it can be used to evaluate the consequences of a new regulation, such as a change in the tick size. On the mathematical side, we formulate the problem as a mixed control-stopping game, with a continuum of players. Under certain structural assumptions, the equilibrium problem splits into two parts: a two-dimensional system of Reflected Backward Stochastic Differential Equations (RBSDEs) and an infinite-dimensional fixed-point equation. Both problems are new and present certain mathematical challenges: the system of RBSDEs has a non-standard reflection, with its components reflecting against functions of each other (which is known as oblique reflection), and the fixed-point equations has a discontinuity. I will show how to overcome these challenges and to prove existence of an equilibrium. I will also demonstrate how to construct an equilibrium LOB in simple examples.

This is joint work with Roman Gayduk.

Date: Monday, February 27, 2017
Time: 4:30 pm
Location: Wean Hall 8220
Submitted by:  Steve Shreve