Department Banner

Events

Equilibrium Model of Limit Order Books and Optimal Execution Problems

Tuesday, January 16, 2018 at 11:40am - 12:40pm

We study the optimal execution problem in an order driven market in which the dynamics of the limit order book exhibits a mean-field type behavior among the sellers. Such a problem will contain two underlying sub-problems: one determines the frontier(the best ask price) and the shape of a limit order book (LOB), followed by one that determines the optimal execution strategy. We show that the best ask price is a competitive equilibrium under the so-called Bertrand competition, characterized by a McKean-Vlasov optimal control problem, from which the shape of the LOB will be determined endogenously. 

The subsequent optimal execution problem will feature an underlying dynamics as a Reflected McKean-Vlasov SDE with Jumps. We shall prove the well-posedness of such SDE, and validate the Dynamic Programming Principle (DPP). We will then show that the value function is a viscosity solution of the corresponding Hamilton-Jacobi-Bellman equation which is in the form of a mean-field type integro-partial-differential quasi-variational inequality.
Contact  TBA
Location   Hill 705

Social Media

Contact Us

HillCenter

Mathematical Finance Master's Program

Department of Mathematics, Hill 348
Hill Center for Mathematical Sciences
Rutgers, The State University of New Jersey
110 Frelinghuysen Road
Piscataway, NJ 08854-8019

Email: finmath (at) rci.rutgers.edu
Phone: +1.848.445.3920
Fax: +1.732.445.5530