When weekly airfare summaries are enough: Sharp risk bounds and decision certificates from aggregated quotes

Abstract Weekly airfare feeds preserve price extrema, means and observation counts, but discard the underlying quote histories. This paper asks which historical risk comparisons remain defensible after that compression. We construct sharp bounds on empirical conditional value-at-risk by retaining both the finite quote count and the requirement that the reported extrema were observed. A majorization argument yields explicit extremal quote vectors; an integer formulation accommodates cent-denominated fares and rounded means. The bounds support itinerary-ranking certificates and exact minimax regret for selecting one alternative. Exhaustive enumeration and 1,400 independent linear-programming solves verify the implementation, followed by 6,000 synthetic aggregation experiments. A case study uses 2,000 Altus records collected over two weeks for Alaska Airlines itineraries departing San Francisco. At the upper-half tail criterion, average identification width falls from USD~14.88 under a support-and-mean relaxation to USD~4.17. Among 182 matched economy return-trip cells, 180 have a certified minimum, versus 174 under the relaxation; three selections differ from the mean-fare rule. The findings support selective investigation of ambiguous comparisons, while establishing no forecast accuracy, realised procurement saving or industry-wide effect.