Semimartingale price systems in models with transaction costs beyond efficient friction

A standing assumption in the literature on proportional transaction costs is efficient friction. Together with robust no free lunch vanishing risk, it rules out strategies of infinite variation, as they usually appear frictionless markets. In this paper, we show how models and without can be unified. The bid ask price a risky asset are given by c\'adl\'ag processes which locally bounded from below may coincide at some points. first step, that if bid-ask model satisfies "no unbounded profit risk" for simple strategies, then there exists semimartingale lying between process. second under additional zeros spread either starting points an excursion away zero or inner right, every predictable strategy specifying amount assets, used to construct corresponding self-financing risk-free position consistent way. Finally, set most general introduced, also provides new view case.