For any sell side trader, optimal liquidation is his bread and butter. Given any client order, the trader has to compete against two forces, market impact and volatility risk.

Market impact : If a large trade is executed too rapidly, costs will be incurred as the trades move the market in an adverse situation

Volatility risk : On the other hand, if the trade is executed too slowly, the the position is subject to risk during the time that the shares remain in the portfolio.
These quantities must be played off against each other by taking in to account the desired performance characteristics of the various participants. I came to know about this paper, years ago, at Courant, by Lee Maclin who works at Pragma. This is a classic paper on execution algorithms. Almgren and Chriss borrow the notion of efficient portfolio frontier and create “Efficient trading frontier” that helps in effective algo execution. At a very high level, the problem is set as a multi constraint optimization problem. A trader minimizes the cost of execution if he minimizes market impact and guards against market volatility. Hence the paper derives Pareto optimal execution paths. These paths give the trader an execution schedule for the order which he can probably feed in to a DMA and automate it. In this document, I will highlight some main points from the paper.
Takeaway :
This paper introduces the idea of “Efficient trading frontier”, a framework for optimal liquidation of portfolios. Portfolio managers always have some kind of efficient frontier thinking behind their strategies. In one sense, such a Markowitz frontier was missing for the “sell side'”. This paper fills that void as the authors explain a framework that can serve as a rough cut quant model to start with. Obviously there are a ton of tweaks that one needs to do in the model to make it a working and practical model. But one must begin somewhere.