Robust No-Free Lunch with Vanishing Risk, a Continuum of Assets and Proportional Transaction Costs

41 Pages Posted: 30 Mar 2013 Last revised: 24 Jun 2015

See all articles by Emmanuel Lepinette

Emmanuel Lepinette

Université Paris-Dauphine - CEREMADE, CNRS

Bruno Bouchard

Université Paris Dauphine - CEREMADE

Erik Taflin

EISTI; University of Cergy-Pontoise

Date Written: January 30, 2013

Abstract

We propose a continuous time model for financial markets with proportional transactions costs and a continuum of risky assets. This is motivated by bond markets in which the continuum of assets corresponds to the continuum of possible maturities. Our framework is well adapted to the study of no-arbitrage properties and related hedging problems. In particular, we extend the Fundamental Theorem of Asset Pricing of Guasoni, Rasonyi and Lepinette (2012) which concentrates on the one dimensional case. Namely, we prove that the Robust No Free Lunch with Vanishing Risk assumption is equivalent to the existence of a Strictly Consistent Price System. Interestingly, the presence of transaction costs allows a natural definition of trading strategies and avoids all the technical and un-natural restrictions due to stochastic integration that appear in bond models without friction. We restrict to the case where exchange rates are continuous in time and leave the general cadlag case for further studies.

Suggested Citation

Lepinette, Emmanuel and Bouchard, Bruno and Taflin, Erik, Robust No-Free Lunch with Vanishing Risk, a Continuum of Assets and Proportional Transaction Costs (January 30, 2013). Available at SSRN: https://ssrn.com/abstract=2240994 or http://dx.doi.org/10.2139/ssrn.2240994

Emmanuel Lepinette (Contact Author)

Université Paris-Dauphine - CEREMADE, CNRS ( email )

Place du Marechal de Lattre de Tassigny
Paris Cedex 16, 75775
France

Bruno Bouchard

Université Paris Dauphine - CEREMADE ( email )

Place du Marechal de Lattre de Tassigny
Paris Cedex 16, 75775
France

Erik Taflin

EISTI ( email )

Avenue du Parc
No Address Available, 95011
France

University of Cergy-Pontoise ( email )

AGM-Dpt mathématiques
2 av. Adolphe Chauvin
Cergy-Pontoise Cedex, 95302
France

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