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摘要翻译：
本文研究了半正定矩阵上的Wishart过程和仿射扩散的模拟。为了做到这一点，我们把重点放在无穷小生成器的分裂上，以便使用Ninomiya和Victoir或Alfonsi这样的合成技术。通过这样做，我们发现了Wishart过程的一个显著的分裂，使我们能够准确地对Wishart分布进行采样，而不受参数的任何限制。它是相关的，但扩展了现有的基于Bartlett分解的精确模拟方法。此外，我们可以构造Wishart过程的高阶离散格式和一般仿射扩散的二阶格式。这些方案在实践中比精确模拟采样整个路径更快。给出了它们收敛性的数值结果。
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英文标题：
《Exact and high order discretization schemes for Wishart processes and
their affine extensions》
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作者：
Abdelkoddousse Ahdida (CERMICS), Aur\'elien Alfonsi (CERMICS)
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最新提交年份：
2013
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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
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一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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英文摘要：
This work deals with the simulation of Wishart processes and affine diffusions on positive semidefinite matrices. To do so, we focus on the splitting of the infinitesimal generator, in order to use composition techniques as Ninomiya and Victoir or Alfonsi. Doing so, we have found a remarkable splitting for Wishart processes that enables us to sample exactly Wishart distributions, without any restriction on the parameters. It is related but extends existing exact simulation methods based on Bartlett's decomposition. Moreover, we can construct high-order discretization schemes for Wishart processes and second-order schemes for general affine diffusions. These schemes are in practice faster than the exact simulation to sample entire paths. Numerical results on their convergence are given.
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PDF链接：
https://arxiv.org/pdf/1006.2281
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