摘要翻译：
过去的索赔经验是计算保险合同公平价格的一个非常重要的信息。例如，在许多欧洲国家，汽车保险的价格取决于司机在过去几年中向保险公司报告的索赔数量。经典地，这些价格是在带有伽马混合分布的混合泊松模型的基础上计算的。混合分布模型的汽车司机素质在整个保险组合。这只是体验评级的一个例子。在经典上下文中，价格等于贝叶斯后验分布的期望。在某些行业（特别是第三方责任和暴露于极端天气事件的行业），我们认为经典的泊松-伽马模型不能很好地描述真实世界的数据。因此，我们研究了混合分布对后验分布的影响，条件是经验的索赔数量。这使得应用其他风险更充分的保费原则比预期原则。本文将反伽马分布作为一种新的混合分布引入索赔数模型，并与经典伽马分布进行了比较。在这两种情况下，都可以找到混合分布的封闭解析表示：在经典情况下是众所周知的负二项分布，在我们的新情况下是使用贝塞尔函数的表示。另外，我们给出了混合泊松-逆伽马分布尾部行为的数值结果。最后介绍了分辨率的概念。它使我们能够决定通过有经验的索赔数量来分类风险组是否是一个风险充分的程序。
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英文标题：
《About the Justification of Experience Rating: Bonus Malus System and a
  new Poisson Mixture Model》
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作者：
Magda Schiegl
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最新提交年份：
2010
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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：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：
  The claim experience of the past is a very important information to calculate the fair price of an insurance contract. In a lot of European countries for instance the prices for motor car insurance depend on the number of claims the driver has reported to the insurance company during the last years. Classically these prices are calculated on the basis of a mixed Poisson model with a gamma mixing distribution. The mixing distribution models the car drivers' qualities across the insured portfolio. This is just one example for experience rating. In the classical context the price is equal to the expectation of the Bayesian posterior distribution.   In some lines of business (especially third party liability and lines with exposure to extreme weather events) we that the real world data cannot be described well enough by the classical Poisson - gamma model. Therefore we investigate the influence of the mixing distribution on the posterior distribution conditional on the experienced number of claims. This enables the application of other - more risk adequate premium principles than the expectation principle. We introduce the inverse - gamma distribution as a new mixing distribution to model claim numbers and compare it to the classical gamma distribution. In both cases a closed analytic representation of the mixed distribution can be found: In the classic case the well known negative binomial distribution, in our new one a representation using the Bessel functions. Additionally we present numerical results about the tail behaviour of the mixed Poisson - inverse - gamma distribution. Finally we introduce the concept of resolution. It enables us to decide if the classification of risk groups via the number of experienced claims is a risk adequate procedure.
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PDF链接：
https://arxiv.org/pdf/1009.4142