超出有效摩擦的带交易成本模型中的半鞅价格系统
Semimartingale price systems in models with transaction costs beyond efficient friction
AI总结：
本文在买卖价由局部下有界右连左极过程给出的模型中，证明满足有界风险无无限利润条件时存在买卖价间的半鞅，并在价差零点附加假设下用其构建自融资头寸，统一了带与不带交易成本的模型。
摘要：
关于比例交易成本的文献中，一个常设假设是有效摩擦（efficient friction）。该假设与稳健的无消失风险免费午餐条件相结合，排除了无摩擦市场中常见的无限变差策略。本文研究了如何统一带交易成本与不带交易成本的模型。风险资产的买价和卖价由局部下有界的cádlág（右连左极）过程给出，二者可能在某些点重合。第一步，我们证明若买卖价差模型对简单策略满足“有界风险下无无限利润”条件，则存在一个介于买价过程与卖价过程之间的半鞅。第二步，在额外假设——即买卖价差的零点要么是偏离零值的游程的起点，要么是右侧内点——之下，我们证明对于每一个指定风险资产数量的有界可料策略，该半鞅可用于以一致的方式构建对应的自融资无风险头寸。最后，本文引入了最具一般性的策略集合，这也为无摩擦情形提供了新的视角。
英文摘要：
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 the ask price of a risky asset are given by cádlág 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 the ask price process. 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.
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