We develop a dynamic equilibrium model for market liquidity. To wit, we solve for the equilibrium prices at which liquidity takers' demands are absorbed by liquidity providers, who can in turn gradually transfer these positions to a group of end users. We also find the optimal strategy of a liquidity taker in such a market and compute the equilibrium price dynamics.

This is a joint work in progress with Peter Bank and Johannes Muhle-Karbe.

Bio: Ibrahim is a Byrne Research Post-Doctoral Assistant Professor in the Department of Mathematics at the University of Michigan. Prior to his arrival at the University of Michigan in September 2017, he was a postdoctoral research at ETH Zurich.

In 2014, he obtained his Ph.D. in mathematics from the University of Southern California, where he worked under the supervision of Prof Jianfeng Zhang. He received his master's degree from Université Pierre et-Marie-Curie, Paris, in 2010 and Diplome d'ingenieur from Ecole Polytechnique in 2009.

In financial mathematics, his research interests include equilibrium and asymptotic results for market illiquidity and optimal transport duality. In stochastic analysis, his work includes viscosity solutions for non-Markovian stochastic systems, Malliavin calculus, rough paths and invariant measures for dispersive SPDEs.