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.
On the completeness of a constrained market / Castagnoli, E; Favero, Gino. - In: INTERNATIONAL JOURNAL OF APPLIED MANAGEMENT SCIENCE. - ISSN 1755-8913. - 1:(2008), pp. 90-96. [10.1504/IJAMS.2008.020041]
On the completeness of a constrained market
FAVERO, Gino
2008-01-01
Abstract
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.| File | Dimensione | Formato | |
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