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I happened to read an article about a problem which said that sometimes traders wants to liquidate their holdings within a fixed time period with minimum market impact. I read that how it can be done optimally.

I would like to know when do conditions arrive when a trader wants to do this? Is this the most general problem which funds face a lot of time ? While they want to invest somewhere else and liquidate their holding positions of some specific securities.

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Liquidating (or buying) a certain amount of an asset in a certain amount of time with minimal market impact is exactly the problem all traders face, whether they are human or algorithmic. If the amount to be traded is large, this can be an interesting problem.

When humans do this, they use their intuition and experience. There are better and worse traders, but no optimal trader.

There are competing algorithms to do this (many are proprietary) because doing it optimally would mean knowing something about the future, which we do not. Normally, these algorithms try to limit the fraction of volume that your trade is taking up---they try and hide your trades in everyone else's but also get it all done in time.

It's a bit of a cat-and-mouse game. Algorithmic and human traders on the other side (and market markers) are constantly scanning the order flow in order to determine if someone is trying to make a large trade so they can react to it. Large trades may indicate a trader who knows something about the stock. If it's a big sale, they may respond by lowering the prices they are willing to pay.

Aside from smart algorithms, a large trader can also try to submit hidden trades in the main market or utilize dark pools. These methods attempt to avoid the usual way traders on the other side monitor the situation. However, smart traders have figured out how to detect this type of behavior too, so I'm not sure how effective this strategy is.

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