In this paper the role of the convexity hipothesys on preferences is analysed. In particular is proved that the set of price functional viable for the set of monotone and continuous preferences is the same than the set of price functionals for the set of preferences that are also convex. This result is given in weaker form for locally convex, Haussdorff t.v.s.
Proving this result allows to build explicitly the convex preference starting from a non convex one. In this way a "minimal" preference relation is defined.
Introducing the definition of sub-gradient for a binary relation, a representation of no-arbitrage price functionals is given.