Published on arxiv:
A note on Almgren-Chriss optimal execution problem with geometric Brownian motion
Abstract: We solve explicitly the Almgren-Chriss optimal liquidation problem where the stock price process follows a geometric Brownian motion. Our technique is to work in terms of cash and to use functional analysis tools. We show that this framework extends readily to the case of a stochastic drift for the price process and the liquidation of a portfolio.
From the announcement:
The 2020 Louis Bachelier Prize is awarded to Professor Mathieu Rosenbaum (École Polytechnique, Paris).
Professor Rosenbaum is internationally recognised as one of the foremost experts in stochastic modelling in finance. Rosenbaum’s research, focused on stochastic processes and their applications in finance, impresses through the breadth of topics it has covered and the depth of results obtained on each topic. His research spans theoretical topics in probability and statistics as well as market microstructure, statistical modelling of high frequency financial data and volatility modelling. His highly visible international profile and remarkable scientific achievements make him an excellent candidate for the 2020 Louis Bachelier Prize.
Published on arxiv:
On bid and ask side-specific tick sizes
Abstract: The tick size, which is the smallest increment between two consecutive prices for a given asset, is a key parameter of market microstructure. In particular, the behavior of high frequency market makers is highly related to its value. We take the point of view of an exchange and investigate the relevance of having different tick sizes on the bid and ask sides of the order book. Using an approach based on the model with uncertainty zones, we show that when side-specific tick sizes are suitably chosen, it enables the exchange to improve the quality of liquidity provision.
