Consistent price systems and arbitrage opportunities of the second kind in models with transaction costs. - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Finance and Stochastics Année : 2011

Consistent price systems and arbitrage opportunities of the second kind in models with transaction costs.

Résumé

In contrast with the classical models of frictionless financial markets, market models with proportional transaction costs, even satisfying usual no-arbitrage properties, may admit arbitrage opportunities of the second kind. This means that there are self-financing portfolios with initial endowments laying outside the solvency region but ending inside. Such a phenomenon was discovered by M. Rasonyi in the discrete-time framework. In this note we consider a rather abstract continuous-time setting and prove necessary and sufficient conditions for the property which we call No Free Lunch of the 2nd Kind, NFL2. We provide a number of equivalent conditions elucidating, in particular, the financial meaning of the property B which appeared as an indispensable 'technical' hypothesis in previous papers on hedging (super-replication) of contingent claims under transaction costs. We show that it is equivalent to another condition on the 'richness' of the set of consistent price systems, close to the condition PCE introduced by Rasonyi. In the last section we deduce the Rasonyi theorem from our general result using specific features of discrete-time models.

Dates et versions

hal-00488288 , version 1 (01-06-2010)

Identifiants

Citer

Emmanuel Denis, Yuri Kabanov. Consistent price systems and arbitrage opportunities of the second kind in models with transaction costs.. Finance and Stochastics, 2011, 16 (1), pp.135-154. ⟨10.1007/s00780-010-0144-6⟩. ⟨hal-00488288⟩
182 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More