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.