Xiaofei will present how to characterize the equilibrium models with limited liquidity through a system of coupled forward-backward SDEs. Although global equilibrium is achieved under specific market dynamics, the nonlinear system of fully-coupled forward-backward SDEs falls outside the scope of any known well-posedness results. We leverage deep-learning techniques to obtain numerical solutions with calibrated parameters to market prices and trading volumes. In the practically relevant large liquidity regime, explicit asymptotic approximations are obtained with interpretable implications to complement deep learning-based numerical algorithms.
Short bio: Xiaofei Shi is an Assistant Professor in the Department of Statistical Sciences at the University of Toronto. Before joining U of T, Xiaofei worked as a Term Assistant Professor at Columbia University. She obtained her PhD in Mathematical Finance at Carnegie Mellon University, under the supervision of Prof. Johannes Muhle-Karbe. Xiaofei is mainly interested in stochastic optimization and stochastic differential equations with applications to mathematical finance. Xiaofei has also worked on various topics in data science, including crowdsourcing, dimensionality reduction, and sparse recovery.