英文标题：
《Stochastic integration with respect to arbitrary collections of
continuous semimartingales and applications to Mathematical Finance》
---
作者：
Constantinos Kardaras
---
最新提交年份：
2019
---
英文摘要：
Stochastic integrals are defined with respect to a collection $P = (P_i; \\, i \\in I)$ of continuous semimartingales, imposing no assumptions on the index set $I$ and the subspace of $\\mathbb{R}^I$ where $P$ takes values. The integrals are constructed though finite-dimensional approximation, identifying the appropriate local geometry that allows extension to infinite dimensions. For local martingale integrators, the resulting space $\\mathsf{S} (P)$ of stochastic integrals has an operational characterisation via a corresponding set of integrands $\\mathsf{R} (C)$, constructed with only reference the covariation structure $C$ of $P$. This bijection between $\\mathsf{R} (C)$ and the (closed in the semimartingale topology) set $\\mathsf{S} (P)$ extends to families of continuous semimartingale integrators for which the drift process of $P$ belongs to $\\mathsf{R} (C)$. In the context of infinite-asset models in Mathematical Finance, the latter structural condition is equivalent to a certain natural form of market viability. The enriched class of wealth processes via extended stochastic integrals leads to exact analogues of optional decomposition and hedging duality as the finite-asset case. A corresponding characterisation of market completeness in this setting is provided.
---
中文摘要：
随机积分是关于连续半鞅的集合$P=（P\\u i；\\，i\\in i）$定义的，不对索引集$i$和$\\mathbb{R}^i$的子空间施加任何假设，其中$P$取值。通过有限维近似构造积分，确定允许扩展到无限维的适当局部几何。对于局部鞅积分器，随机积分的结果空间$\\ mathsf{S}（P）$通过一组相应的被积函数$\\ mathsf{R}（C）$具有操作特征，该被积函数仅参考P$的协变结构$\\ C$。$\\ mathsf{R}（C）$和（半鞅拓扑中闭合的）集$\\ mathsf{S}（P）$之间的这种双射扩展到了连续半鞅积分器族，其中$P$的漂移过程属于$\\ mathsf{R}（C）$。在数学金融中的无限资产模型中，后一种结构条件相当于市场生存能力的某种自然形式。通过扩展的随机积分，财富过程的丰富类可以精确模拟有限资产情况下的可选分解和对冲对偶。在此设置中提供了相应的市场完整性特征。
---
分类信息：

一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
--
一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
--

---
PDF下载：
-->