Abstract: We address the mechanism of a principal-agent approach, based on a stochastic bilevel optimization, applied to an exchange setting suitable make-take fees to attract liquidity on its platform. We provide the optimal compensation scheme proposed to a market maker together with the optimal quotes he should display by using a dynamic programming principle together with standard tools in stochastic control. The simplicity of our formulas allows us to analyze in details the effects of optimal contracting with an exchange, compared to a situation without contract. We show in particular that it improves liquidity and reduces trading costs for investors. We then extend the study to a market maker acting at the same time in different trading pools of an exchange. In this case, we design deep reinforcement learning algorithms enabling us to approximate efficiently the optimal controls of the market maker and the optimal incentives to be provided by the exchange.

Bio: I have obtained my PhD in December 2015 at Université Paris-Dauphine on stochastic analysis and Backward Stochastic Differential Equations. Since September 2016 I am assistant professor at Ecole Polytechnique in probability and financial mathematics. My research interests are stochastic differential games, mean field games, stochastic control, contract theory, market microstructure, population monitoring.