摘要翻译：
我们建立了一类非寿险准备金模型，使用稳定的1/2随机桥来模拟已付索赔的累积，允许对最终损失的先验分布进行本质上任意的选择。采用基于信息的方法对保留问题进行研究，导出了最终损失的条件分布过程。通过对最终损失的条件期望给出了“最佳估计最终损失过程”。我们导出了最优估计最终损失过程的显式表达式，以及从总损失超额再保险条约中产生的预期赔偿的显式表达式。使用确定性的时间变化允许匹配支付索赔的任何初始（增加）发展模式。我们证明了这些方法非常适合于在发生灾难性损失的概率很小的情况下的索赔建模。广义逆高斯(GIG)分布是先验极限损耗分布的自然选择。对于特定的GIG参数选择，最优估计最终损失过程可以写成有偿索赔过程的有理函数。我们将模型扩展为包括第二个支付索赔过程，并允许这两个过程相互依赖。所得结果可应用于多行业或多起源年份的建模。多维模型具有计算维数保持较低的特性，无论支付索赔过程的数量如何。提出了一种模拟支付索赔过程的算法。
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英文标题：
《Stable-1/2 Bridges and Insurance》
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作者：
Edward Hoyle, Lane P. Hughston, Andrea Macrina
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最新提交年份：
2014
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：General Finance        一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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英文摘要：
  We develop a class of non-life reserving models using a stable-1/2 random bridge to simulate the accumulation of paid claims, allowing for an essentially arbitrary choice of a priori distribution for the ultimate loss. Taking an information-based approach to the reserving problem, we derive the process of the conditional distribution of the ultimate loss. The "best-estimate ultimate loss process" is given by the conditional expectation of the ultimate loss. We derive explicit expressions for the best-estimate ultimate loss process, and for expected recoveries arising from aggregate excess-of-loss reinsurance treaties. Use of a deterministic time change allows for the matching of any initial (increasing) development pattern for the paid claims. We show that these methods are well-suited to the modelling of claims where there is a non-trivial probability of catastrophic loss. The generalized inverse-Gaussian (GIG) distribution is shown to be a natural choice for the a priori ultimate loss distribution. For particular GIG parameter choices, the best-estimate ultimate loss process can be written as a rational function of the paid-claims process. We extend the model to include a second paid-claims process, and allow the two processes to be dependent. The results obtained can be applied to the modelling of multiple lines of business or multiple origin years. The multi-dimensional model has the property that the dimensionality of calculations remains low, regardless of the number of paid-claims processes. An algorithm is provided for the simulation of the paid-claims processes.
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PDF链接：
https://arxiv.org/pdf/1005.0496