Please join the Department of Applied Mathematics on Tuesday, March 25, 2025, at 10–11 a.m. in the John T. Rettaliata Engineering Center, room 119, for a seminar. Speaker Thibaut Mastrolia, assistant professor of industrial engineering and operations research at UC Berkeley, will give a talk titled “Optimal Rebate Design: Incentives, Competition and Efficiency in Auction Markets.”

Abstract

This talk explores the design of an efficient rebate policy in auction markets, focusing on a continuous-time setting with competition among market participants. In this model, a stock exchange collects transaction fees from auction investors executing block trades to buy or sell a risky asset, then redistributes these fees as rebates to competing market makers submitting limit orders. Market makers influence both the price at which the asset trades and their arrival intensity in the auction. We frame this problem as a principal-multi-agents problem and provide necessary and sufficient conditions to characterize the Nash equilibrium among market makers. The exchange’s optimization problem is formulated as a high-dimensional Hamilton-Jacobi-Bellman equation with Poisson jump processes, which is solved using a verification result. To numerically compute the optimal rebate and transaction fee policies, we apply the Deep BSDE method. Our results show that optimal transaction fees and rebate structures improve market efficiency by narrowing the spread between the auction clearing price and the asset’s fundamental value, while ensuring a minimal gain for both market makers indexed on the asset price on a coexisting limit order book. Joint work with Tianrui Xu (UC Berkeley).