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We show that the lack of arbitrage in a model with both fixed andproportional transaction costs is equivalent to the existence of a family ofabsolutely continuous single-step probability measures, together with anadapted process with values between the bid-ask spreads that satisfies themartingale property with respect to each of the measures. This extends Harrisonand Pliska's classical Fundamental Theorem of Asset Pricing to the case ofcombined fixed and proportional transaction costs.

Fundamental Theorem of Asset Pricing under fixed and proportional transaction costs