On the completeness of a constrained market

We show how the well-known Farkas Lemma, commonly used to characterise absence of arbitrages in perfect markets, is also exploitable to ascertain the completeness of a market with total short sales constraints. The generalisation of this lemma to convex cones also allows to characterise the completeness of a market with general conic constraints on investment strategies. Such results can be also applied to tell whether it is possible to hedge perfectly any risky position with a given set of tools.