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We propose a continuous time model for financial markets with proportionaltransactions costs and a continuum of risky assets. This is motivated by bondmarkets in which the continuum of assets corresponds to the continuum ofpossible maturities. Our framework is well adapted to the study of no-arbitrageproperties and related hedging problems. In particular, we extend theFundamental Theorem of Asset Pricing of Guasoni, R\'asonyi and L\'epinette(2012) which concentrates on the one dimensional case. Namely, we prove thatthe Robust No Free Lunch with Vanishing Risk assumption is equivalent to theexistence of a Strictly Consistent Price System. Interestingly, the presence oftransaction costs allows a natural definition of trading strategies and avoidsall the technical and un-natural restrictions due to stochastic integrationthat appear in bond models without friction. We restrict to the case whereexchange rates are continuous in time and leave the general c\`adl\`ag case forfurther studies.

Robust no-free lunch with vanishing risk, a continuum of assets and proportional transaction costs