FRE Special Seminar: Thibaut Mastrolia and Valentin Tissot-Daguette

3 pm | Thibaut Mastrolia

Title

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).

Bio

Thibaut Mastrolia defended his PhD in applied mathematics at the University of Paris-Dauphine in 2015. He was an assistant professor at Ecole Polytechnique from 2016 to 2021. Since September 2021, he has been an assistant professor at UC Berkeley in the Department of Industrial Engineering and Operations Research. His current research interests include market microstructure and financial regulation, population monitoring and natural resource management, stochastic control, moral hazard contract theory, stochastic differential games, and mean field games. He was awarded in 2023 by the France-Berkeley fund for the project “Cyber risk mathematical modeling.

4 pm | Valentin Tissot-Daguette

Title

Occupied Processes in Finance

Bio

Valentin Tissot-Daguette is a quantitative researcher in the CTO office at Bloomberg. He obtained his PhD degree from the Operations Research and Financial Engineering department at Princeton University in 2024, under the supervision of Prof. Mete Soner and Bruno Dupire. Prior to his PhD, Valentin studied at EPFL and ETH Zurich in Switzerland where he completed a Bachelor's degree in Mathematics and a Master's degree in Financial Engineering. His research interests include exotic derivatives, free boundary problems, and stochastic optimal control.

Abstract

We study a Markovian framework for path dependence based on occupied processes, which records the time spent by the underlying path at arbitrary levels. The associated calculus strikes a middle ground between the classical setting and Dupire's functional Itô calculus. We extend Itô's formula by introducing the occupation derivative, and we recast through Feynman-Kac's theorem a large class of path-dependent PDEs as parabolic problems where the occupation flow plays the role of time.

We demonstrate the omnipresence of occupied processes in finance, and discuss applications in financial modeling where the occupation flow dictates the asset price dynamics. The diffusion coefficient, termed occupied volatility, leads to a sub-class of path-dependent volatility models that can be effectively simulated.

This presentation is partly based on joint work with Mete Soner (Princeton University) and Jianfeng Zhang (USC).