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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.

This problem sounds like it should be standard, but I don't know where to look. The problem formulation reminds me of portfolio optimization problems, but I am no expert in the field. Any pointers to the literature where this specific problem is discussed are appreciated.

Edit: Thanks to Bjørn Kjos-Hanssen's answer I now see that it is more related to optimal stopping rather than portfolio optimization.

Edit 2: I have also asked the question on stackexchange, but have not received any feedback:

https://math.stackexchange.com/questions/3034583/reference-request-in-optimal-stopping

Please re-open the question here!

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    $\begingroup$ Are you allowed to sell, as well, during the day? $\endgroup$
    – Bjørn Kjos-Hanssen
    Commented Nov 30, 2018 at 6:36
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    $\begingroup$ Can the people who have downvoted this question please explain why? I consider this a perfectly fine question. $\endgroup$
    – Bettina Kraus
    Commented Nov 30, 2018 at 9:17
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    $\begingroup$ Maybe people are interpreting the phrase "problem formulation" to mean that it's a homework question and therefore not a research level question? ... Anyway I think it's a very interesting question $\endgroup$
    – Bjørn Kjos-Hanssen
    Commented Nov 30, 2018 at 14:19
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    $\begingroup$ I second @BjørnKjos-Hanssen's comment. This is not my area, but it seems to me that at worst, this is a question which could be improved/enhanced with some more specific information about the context in which the problem arose. $\endgroup$
    – Yemon Choi
    Commented Dec 1, 2018 at 20:44
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    $\begingroup$ @YemonChoi The question is more or less exactly the problem that was posed to us by one of our customers (a power supply company). I was checking the literature in search for an answer and was unable to find anything similar enough to move forward from there. For the people who claim that this problem is not research level it should be easy to point me to a textbook or paper where this problem is solved. $\endgroup$
    – Bettina Kraus
    Commented Dec 2, 2018 at 10:21

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It seems related to optimal stopping. First you have to decide when to make the first purchase. Then you have a new problem of when to make the next purchase.

Although it's more complicated than that because you also have to decide how much to buy, when you do buy.

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