英文标题：
《Affine representations of fractional processes with applications in
mathematical finance》
---
作者：
Philipp Harms and David Stefanovits
---
最新提交年份：
2018
---
英文摘要：
Fractional processes have gained popularity in financial modeling due to the dependence structure of their increments and the roughness of their sample paths. The non-Markovianity of these processes gives, however, rise to conceptual and practical difficulties in computation and calibration. To address these issues, we show that a certain class of fractional processes can be represented as linear functionals of an infinite dimensional affine process. This can be derived from integral representations similar to those of Carmona, Coutin, Montseny, and Muravlev. We demonstrate by means of several examples that this allows one to construct tractable financial models with fractional features.
---
中文摘要：
分数过程由于其增量的依赖结构和样本路径的粗糙性，在金融建模中得到了广泛应用。然而，这些过程的非马尔可夫性给计算和校准带来了概念和实际困难。为了解决这些问题，我们证明了一类分数过程可以表示为无限维仿射过程的线性泛函。这可以从类似于卡莫纳、库廷、蒙塞尼和穆拉夫列夫的积分表示中推导出来。我们通过几个例子证明，这允许我们构造具有分数特征的可处理金融模型。
---
分类信息：

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
--
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
--

---
PDF下载：
-->