We model sequential auctions in financial markets during a given time period receiving orders of market participants. A clearing price of the auction is determined as the price maximizing the exchanged volume at the clearing time according to the supply and demand of each market participant. We then focus on the optimal duration of an auction to reduce the error between the clearing price and the efficient price of the stock considered. When investors are strategic, they minimize simultaneously their transaction costs by adapting their trading intensities to the market state. We thus provide the existence of a Nash equilibrium for this stochastic game reduced to the analysis of a system of PDE with discontinuities. We then compute the optimal duration of the auctions for some stocks traded on Euronext and compare the quality of price formation process under this optimal value to the case of a continuous limit order book. We then extend the study to a new market mechanism "ad hoc electronic auction design" (AHEAD) in which market participants have the opportunity to trigger the auction when necessary in addition to controlling their trading intensities. We prove in particular that this model is well-posed and we compare it with classical sequential auctions and limit order books.
Short bio: I defended my PhD in applied mathematics at the University of Paris-Dauphine in 2015. I was an assistant professor at Ecole Polytechnique from 2016 to 2021. Since September 2021, I have been an assistant professor at UC Berkeley in the Department of Industrial Engineering and Operations Research. My 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.