Almgren and Chriss ("Optimal execution of portfolio transactions", Journal of Risk, Vol. 3, No. 2, 2010, pp. 5-39) and Lehalle ("Rigorous strategic trading: balanced portfolio and mean reversion", Journal of Trading, Summer 2009, pp. 40-46.) developed optimal trading algorithms for assets and...

The efficient frontier is a core concept in Modern Portfolio Theory. Based on this idea, we will construct optimal trading curves for different types of portfolios. These curves correspond to the algorithmic trading strategies that minimize the expected transaction costs, i.e. the joint effect...

We extend the market-making models with inventory constraints of Avellaneda and Stoikov ("High-frequency trading in a limit-order book", Quantitative Finance Vol.8 No.3 2008) and Gueant, Lehalle and Fernandez-Tapia ("Dealing with inventory risk", Preprint 2011) to the case of a rather general...

Automated Market Makers (AMMs) are the main liquidity providers in the Decentralised Finance (DeFi) space. They are programmes that follow some coded rules to determine and adjust prices and volumes. Amongst those rules, the most common one is the constant-product formula, which is followed by...

Evolutions of the trading landscape lead to the capability to exchange the same financial instrument on different venues. Because of liquidity issues, the trading firms split large orders across several trading destinations to optimize their execution. To solve this problem we devised two...

Considering that a trader or a trading algorithm interacting with markets during continuous auctions can be modeled by an iterating procedure adjusting the price at which he posts orders at a given rhythm, this paper proposes a procedure minimizing his costs. We prove the a.s. convergence of the...

Market makers continuously set bid and ask quotes for the stocks they have under consideration. Hence they face a complex optimization problem in which their return, based on the bid-ask spread they quote and the frequency at which they indeed provide liquidity, is challenged by the price risk...

This paper addresses the optimal scheduling of the liquidation of a portfolio using a new angle. Instead of focusing only on the scheduling aspect like Almgren and Chriss, or only on the liquidity-consuming orders like Obizhaeva and Wang, we link the optimal trade-schedule to the price of the...