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摘要翻译：
在数学金融和随机过程的其他应用中，常常存在特征函数可能已知，但密度函数的显式形式却不可用的情况。分位数函数的知识极大地促进了任何分布的模拟，通过分位数函数，均匀分布的样本可以转换为给定分布的样本。本文在没有明确的密度知识的情况下，直接从概率分布的特征函数来分析分位数函数的计算。我们构造了一个非线性积分微分方程，尽管它的复杂性，但它允许关于中值的分位数幂级数的迭代解。我们给出了一些例子，包括尾部模型，并展示了如何为例子生成C代码。
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英文标题：
《Monte Carlo sampling given a Characteristic Function: Quantile Mechanics
in Momentum Space》
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作者：
William T. Shaw, Jonathan McCabe
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最新提交年份：
2009
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分类信息：
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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一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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英文摘要：
In mathematical finance and other applications of stochastic processes, it is frequently the case that the characteristic function may be known but explicit forms for density functions are not available. The simulation of any distribution is greatly facilitated by a knowledge of the quantile function, by which uniformly distributed samples may be converted to samples of the given distribution. This article analyzes the calculation of a quantile function direct from the characteristic function of a probability distribution, without explicit knowledge of the density. We form a non-linear integro-differential equation that despite its complexity admits an iterative solution for the power series of the quantile about the median. We give some examples including tail models and show how to generate C-code for examples.
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PDF链接：
https://arxiv.org/pdf/0903.1592
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