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A standing assumption in the literature on proportional transaction costs isefficient friction. Together with robust no free lunch with vanishing risk, itrules out strategies of infinite variation, as they usually appear infrictionless markets. In this paper, we show how the models with and withouttransaction costs can be unified.  The bid and the ask price of a risky asset are given by c\'adl\'ag processeswhich are locally bounded from below and may coincide at some points. In afirst step, we show that if the bid-ask model satisfies "no unbounded profitwith bounded risk" for simple strategies, then there exists a semimartingalelying between the bid and the ask price process.  In a second step, under the additional assumption that the zeros of thebid-ask spread are either starting points of an excursion away from zero orinner points from the right, we show that for every bounded predictablestrategy specifying the amount of risky assets, the semimartingale can be usedto construct the corresponding self-financing risk-free position in aconsistent way. Finally, the set of most general strategies is introduced,which also provides a new view on the frictionless case.

Semimartingale price systems in models with transaction costs beyond efficient friction