Constructing minimum-width confidence bands

•We construct minimum-width confidence bands from a sample of paths.•The algorithm is based on mixed-integer optimization.•It is guaranteed that the globally optimal solution is found.•For very large problems, the algorithm also provides a fast approximation.

We construct minimum-width confidence bands with a predefined nominal coverage from a finite set of sample paths. In contrast to the several heuristics suggested in the literature, our mixed-integer optimization algorithm calculates global minimum-width pathwise confidence bands. For very large problems, our solution can be used as an approximation with a bounded and known gap to the globally optimal solution.