Quantile Diffusions for Risk Analysis
Quantile Diffusions for Risk Analysis
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DOI：
10.2139/ssrn.3508702
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发表时间：
2019-12
期刊：
影响因子：
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通讯作者：
Holly Brannelly;A. Macrina;G. Peters
中科院分区：
文献类型：
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作者：
Holly Brannelly;A. Macrina;G. Peters
本文着重于一类新的扩散过程，允许直接和动态建模的分位数扩散的发展。我们构造了分位数扩散过程，通过将给定的单变量扩散过程的每个边缘在由分布函数和分位数函数组成的复合映射下进行变换，从而产生所得到的分位数过程的边缘。变换允许关于变换的参数直接解释基础过程的时刻。例如，可以引入偏度或峰度，以实现对诸如金融资产回报的数据的更现实的建模，以及对基础过程的样本的再循环，以使变换的分位数过程的模拟更容易。我们得到了分位数扩散所满足的随机微分方程，并讨论了分位数扩散的一般情形和更具体的Tukey $g$-$h$，$g$-变换和$h$-变换族的强解和弱解存在的条件.
This paper focuses on the development of a new class of diffusion processes that allows for direct and dynamic modelling of quantile diffusions. We constructed quantile diffusion processes by transforming each marginal of a given univariate diffusion process under a composite map consisting of a distribution function and quantile function, which in turn produces the marginals of the resulting quantile process. The transformation allows for the moments of the underlying process to be directly interpreted with regard to parameters of the transformation. For instance, skewness or kurtosis may be introduced to enable more realistic modelling of data such as financial asset returns, as well as the recycling of samples of the underlying process to make simulation of the transformed quantile process easier. We derive the stochastic differential equation satisfied by the quantile diffusion, and characterise the conditions under which strong and weak solutions exist, both in the general case and for the more specific Tukey $g$-$h$, $g$-transform and $h$-transform families of quantile diffusions.