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I am given the following task. Distributed over a trading day, I am supposed to buy a certain quantity of a good. The price of this good changes during the day. The goal is to buy the required quantity at the minimum total cost.

Any pointers to the literature where this specific problem is discussed are appreciated.

I asked this question before on mathoverflow, but the question was closed:

https://mathoverflow.net/questions/316550/reference-request-in-optimal-stopping

I got the hint there that it may be related to optimal stopping problems, however I could not find this exact problem anywhere in the literatute yet.

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See bib of this presentation for some example references to market impact models.

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