论文标题
ITô随机差异
Itô Stochastic differentials
论文作者
论文摘要
对于连续的semimartingale $ x $，在时间$ t $的情况下，我们给符号$ dx_t $提供了无限的含义。我们在时间$ t $的差速器空间上定义了矢量空间结构，并推断了与经典的ITô集成理论一致的关键属性。特别是，我们通过微积分的基本定理的随机版本将差异的概念与ITô集成联系起来。我们的差异遵循链条规则的版本，这是ITô引理的本地版本。我们将结果应用于金融数学，以立即及时提供投资组合理论。
We give an infinitesimal meaning to the symbol $dX_t$ for a continuous semimartingale $X$ at an instant in time $t$. We define a vector space structure on the space of differentials at time $t$ and deduce key properties consistent with the classical Itô integration theory. In particular, we link our notion of a differential with Itô integration via a stochastic version of the Fundamental Theorem of Calculus. Our differentials obey a version of the chain rule, which is a local version of Itô's lemma. We apply our results to financial mathematics to give a theory of portfolios at an instant in time.
