【摘要】 本文在极值理论的POT模型基础上,建立了基于分维的POT幂律模型,给出了POT模型的阈值选择的理论解释,还给出了满足尾部分布适合幂律的条件。分析表明,此模型较已有方法能更方便地估计尾部参数,对小样本情形研究厚尾问题提供了新的思路。此外,为计算操作风险损失和的在险价值(VaR)问题,本文引入保险理论里的随机和模型,并给出了计算操作风险在险值的简化公式。更多还原

【Abstract】 In this paper,a new POTPL(POT-Power Law)model on the basis of fractal dimension theory by using POT model of extreme value theory is presented.It gives not only a theoretical explanation for the choice of the threshold of POT model,but also satisfying power law condition of estimating tail disfribution.The analysis result shows that this model can be more convenient to estimate the tail than former methods.And it provides a new idea for solving fat-tail problem in small-sample circumstances,In addition,the random sum model in insurance is introduced in order to solve calculating Sum VaR of the banking operational risk losses.Then a simplified formula of VaR is given on the basis of operational loss data in our banks.更多还原