

























Shafer and Vovk introduce in their book \cite{ShaferVovk:2018} the notion of \emph{instant enforcement} and \emph{instantly blockable} properties. However, they do not associate these notions with any outer measure, unlike what Vovk did in the case of sets of ''typical'' price paths. In this paper we introduce an outer measure on the space $[0, +\ns) \times Ω$ which assigns zero value exactly to those sets (properties) of pairs of time $t$ and an elementary event $ω$ which are instantly blockable. Next, for a slightly modified measure, we prove Itô's isometry and BDG inequalities, and then use them to define an Itô-type integral. Additionally, we prove few properties for the quadratic variation of model-free, continuous martingales, which hold with instant enforcement.
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。