摘要翻译：
由于风险之间依赖结构的不确定性，分散风险的收益难以定量估计。此外，多维依赖关系的建模也是一项重要的任务。本文主要研究了一种投资组合聚集的技术，即树内风险聚集，在聚集的每一步都通过Copula设置依赖关系。我们严格地定义了这个过程，然后广泛地研究了任意大小和形状的高斯树，其中个体风险是正常的，并且使用了高斯copula。我们导出了高斯树的多样化效益作为其形状和依赖参数的函数的精确分析结果。这种聚合树的“玩具模型”使人们在以这种方式聚合风险时能够理解基本现象的作用。特别地，它表明，对于固定数量的个体风险，“瘦”树比“胖”树更好地多样化。与此相关的是，分层树具有相对于在聚合的每一步选择的依赖参数降低总体依赖的自然趋势。我们还证明了这些结果在高斯世界之外的更一般情况下成立，并显著地应用于更现实的投资组合（对数正态树）。我们认为，任何使用这种工具的保险公司或再保险公司都应该意识到这些系统的影响，这种意识应该强烈要求设计足够适合业务的树。最后，我们讨论了确定风险之间的全部共同分配的问题。我们证明了分层机制既不要求也不指定联合分布，但后者可以通过在风险与其和之间添加条件独立性假设来精确地确定（在高斯情况下）。
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英文标题：
《Copula-based Hierarchical Aggregation of Correlated Risks. The behaviour
  of the diversification benefit in Gaussian and Lognormal Trees》
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作者：
Jean-Philippe Bruneton
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最新提交年份：
2011
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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：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Quantitative Finance        数量金融学
二级分类：Portfolio Management        项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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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 benefits of diversifying risks are difficult to estimate quantitatively because of the uncertainties in the dependence structure between the risks. Also, the modelling of multidimensional dependencies is a non-trivial task. This paper focuses on one such technique for portfolio aggregation, namely the aggregation of risks within trees, where dependencies are set at each step of the aggregation with the help of some copulas. We define rigorously this procedure and then study extensively the Gaussian Tree of quite arbitrary size and shape, where individual risks are normal, and where the Gaussian copula is used. We derive exact analytical results for the diversification benefit of the Gaussian tree as a function of its shape and of the dependency parameters.   Such a "toy-model" of an aggregation tree enables one to understand the basic phenomena's at play while aggregating risks in this way. In particular, it is shown that, for a fixed number of individual risks, "thin" trees diversify better than "fat" trees. Related to this, it is shown that hierarchical trees have the natural tendency to lower the overall dependency with respect to the dependency parameter chosen at each step of the aggregation. We also show that these results hold in more general cases outside the gaussian world, and apply notably to more realistic portfolios (LogNormal trees). We believe that any insurer or reinsurer using such a tool should be aware of these systematic effects, and that this awareness should strongly call for designing trees that adequately fit the business.   We finally address the issue of specifying the full joint distribution between the risks. We show that the hierarchical mechanism does not require nor specify the joint distribution, but that the latter can be determined exactly (in the Gaussian case) by adding conditional independence hypotheses between the risks and their sums.
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PDF链接：
https://arxiv.org/pdf/1111.1113