Semimartingale price systems in models with transaction costs beyond efficient friction
统一了有摩擦和无摩擦市场模型，在比例交易成本下，通过引入半鞅价格过程，证明了在无界风险限制下存在半鞅介于买卖价之间，并构建了自融资策略。
Abstract A standing assumption in the literature on proportional transaction costs is efficient friction. Together with robust no free lunch with vanishing risk, it rules out strategies of infinite variation as they usually appear in frictionless markets. In this paper, we show how the models with and without transaction costs can be unified. The bid and ask prices of a risky asset are given by càdlàg processes which are locally bounded from below and may coincide at some points. In a first step, we show that if the bid–ask model satisfies “no unbounded profit with bounded risk” for simple strategies, then there exists a semimartingale lying between the bid and ask price processes. In a second step, under the additional assumption that the zeros of the bid–ask spread are either starting points of an excursion away from zero or inner points from the right, we show that for every bounded predictable strategy specifying the amount of risky assets, the semimartingale can be used to construct the corresponding self-financing risk-free position in a consistent way. Finally, the set of most general strategies is introduced, which also provides a new view on the frictionless case.