Constant product markets with concentrated liquidity (CL) are the most popular type of
automated market makers. In this paper, we characterize the continuous-time wealth …

This review article is intended to collect and summarize many of the results in the field of
optimal execution over the last twenty years. In doing so, we describe the general workings …

Automated market makers (AMMs) are a new prototype of trading venues which are
revolutionising the way market participants interact. At present, the majority of AMMs are …

We show how traders use marketable limit orders (MLOs) to liquidate a position over a
trading window when there is latency in the marketplace. MLOs are liquidity-taking orders …

Trading frictions are stochastic. They are, moreover, in many instances fast mean-reverting.
Here, we study how to optimally trade in a market with stochastic price impact and study …

In this paper, we provide a closed-form solution to an optimal portfolio execution problem
with stochastic price impact and stochastic net demand pressure. Specifically, each trade of …

Optimal execution is an important problem faced by any trader. Most solutions are based on
the assumption of constant market impact, while liquidity is known to be dynamic. Moreover …

A novel high-frequency market making approach in discrete time is proposed that admits
closed-form solutions. By taking advantage of demand functions that are linear in the quoted …

Latency is the time delay between an exchange streaming market data to a trader, the trader
processing information and deciding to trade, and the exchange receiving the order from the …

We propose the macroscopic market making model\a la Avellaneda-Stoikov, using
continuous processes for orders instead of discrete point processes. The model intends to …