Journal article: We study the convexity property of the set Q[subscript F] of arbitrage-free prices of a multi-period financial structure F. The set of arbitrage-free prices is shown to be a convex cone under conditions on the financial structure F that hold in particular for short-lived assets. Furthermore, we provide examples of equivalent financial structures F and F' such that Q[subscript F] is a convex cone, but Q[subscript F'] is neither convex nor a cone.