英文标题：
《Risk Margin Quantile Function Via Parametric and Non-Parametric Bayesian
  Quantile Regression》
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作者：
Alice X.D. Dong, Jennifer S.K. Chan, Gareth W. Peters
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最新提交年份：
2014
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英文摘要：
  We develop quantile regression models in order to derive risk margin and to evaluate capital in non-life insurance applications. By utilizing the entire range of conditional quantile functions, especially higher quantile levels, we detail how quantile regression is capable of providing an accurate estimation of risk margin and an overview of implied capital based on the historical volatility of a general insurers loss portfolio. Two modelling frameworks are considered based around parametric and nonparametric quantile regression models which we develop specifically in this insurance setting.   In the parametric quantile regression framework, several models including the flexible generalized beta distribution family, asymmetric Laplace (AL) distribution and power Pareto distribution are considered under a Bayesian regression framework. The Bayesian posterior quantile regression models in each case are studied via Markov chain Monte Carlo (MCMC) sampling strategies.   In the nonparametric quantile regression framework, that we contrast to the parametric Bayesian models, we adopted an AL distribution as a proxy and together with the parametric AL model, we expressed the solution as a scale mixture of uniform distributions to facilitate implementation. The models are extended to adopt dynamic mean, variance and skewness and applied to analyze two real loss reserve data sets to perform inference and discuss interesting features of quantile regression for risk margin calculations.
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中文摘要：
我们开发分位数回归模型，以得出风险边际，并评估非寿险应用中的资本。通过利用整个条件分位数函数范围，尤其是更高的分位数水平，我们详细介绍了分位数回归如何能够根据一般保险公司损失投资组合的历史波动率提供准确的风险边际估计和隐含资本概述。我们考虑了两个基于参数和非参数分位数回归模型的建模框架，这两个模型是我们在本保险环境中专门开发的。在参数分位数回归框架下，在贝叶斯回归框架下考虑了柔性广义贝塔分布族、非对称拉普拉斯分布和幂帕累托分布等模型。通过马尔可夫链蒙特卡罗（MCMC）抽样策略研究了每种情况下的贝叶斯后分位数回归模型。与参数贝叶斯模型相比，在非参数分位数回归框架中，我们采用了一个AL分布作为代理，并与参数AL模型一起，将解表示为均匀分布的比例混合，以便于实现。将模型扩展为采用动态均值、方差和偏态，并应用于分析两个实际损失准备金数据集，以进行推理，并讨论分位数回归在风险边际计算中的有趣特征。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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一级分类：Statistics        统计学
二级分类：Applications        应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
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一级分类：Statistics        统计学
二级分类：Computation        计算
分类描述：Algorithms, Simulation, Visualization
算法、模拟、可视化
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