Title: On the completeness of a constrained market

Authors: Erio Castagnoli, Gino Favero

Addresses: Universita Commerciale 'Luigi Bocconi', Dipartimento di Scienza delle Decisioni, via Roentgen 1, 20136 Milano, Italy. ' Universita Commerciale 'Luigi Bocconi', Dipartimento di Finanza, via Roentgen 1, 20136 Milano, Italy

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.

Keywords: market completeness; short-sale constraints; Farkas Lemma; constrained markets; investment strategies; hedging.

DOI: 10.1504/IJAMS.2008.020041

International Journal of Applied Management Science, 2008 Vol.1 No.1, pp.90 - 96

Published online: 21 Aug 2008 *

Full-text access for editors Access for subscribers Purchase this article Comment on this article