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Market making literature and models often include a factor for 'terminal time' (1), (2) within which the market maker's inventory is liquidated.

What is the reasoning behind this idea? Is it simply to deal with close of market, or is there some other unwritten rule?

(1) http://stanford.edu/class/msande448/2018/Final/Reports/gr5.pdf

(2) https://arxiv.org/pdf/1602.00358.pdf

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    $\begingroup$ Thats because a lot of market makers flatten their positions at EOD. So the literature assumes that whatever positions the MM has at that point is squared off using market orders. Hence, terminal time. $\endgroup$ – nimbus3000 Feb 20 at 15:18
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The real reason for the literature you're seeing is that constrained optimization problems are often much easier to solve and give rise to simpler, more elegant results or tractable analytical solutions. It's entirely a mathematical motivation, not a practical one.

The "cop-out" reason (which is not completely invalid) they give to justify the terminal constraint is that: As a market maker, you generally want to have low margin requirements or large credit arrangements with your prime broker(s). This way you require less operating capital, and you can leave more orders open and generally increase your trading volume. You pose a much lower credit risk to your prime broker(s) when you carry no risk or positions overnight, so many market makers seek to flatten their positions before end of day.

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