论文标题
用分数布朗运动的积分解决方案不同的赫斯特指数
Solution of integrals with fractional Brownian motion for different Hurst indices
论文作者
论文摘要
在本文中，我们将评估定义所有相关Hurst索引（即（0,1）$的$ H \ $ h \ in（0,1）$的分数布朗运动（FBM），随机过程的条件期望，方差和特征功能。例如，分数Ornstein-uhlenbeck（FOU）过程产生高度非平凡的整合公式，在考虑整个Hurst索引范围时，需要仔细分析。我们将表明，从复杂分析中，分析延续的经典技术提供了一种扩展积分有效性领域的方法，从$ h \ in（1/2,1）$，较大的域，$ h \ in（0,1）$。不同HURST指数的数值实验证实了此处介绍的积分制剂的鲁棒性和效率。此外，在傅立叶余弦扩展的帮助下，我们为与FOU流程相关的流程提供准确且高效的财务选择定价结果。
In this paper, we will evaluate integrals that define the conditional expectation, variance and characteristic function of stochastic processes with respect to fractional Brownian motion (fBm) for all relevant Hurst indices, i.e. $H \in (0,1)$. The fractional Ornstein-Uhlenbeck (fOU) process, for example, gives rise to highly nontrivial integration formulas that need careful analysis when considering the whole range of Hurst indices. We will show that the classical technique of analytic continuation, from complex analysis, provides a way of extending the domain of validity of an integral, from $H\in(1/2,1)$, to the larger domain, $H\in(0,1)$. Numerical experiments for different Hurst indices confirm the robustness and efficiency of the integral formulations presented here. Moreover, we provide accurate and highly efficient financial option pricing results for processes that are related to the fOU process, with the help of Fourier cosine expansions.
