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The Aggregate Risk and Completely Mixable Distributions

总风险和完全混合分布

基本信息

批准号：
435844-2013
负责人：
Wang, Ruodu
金额：
$ 1.17万
依托单位：
University of Waterloo
依托单位国家：
加拿大
项目类别：
Discovery Grants Program - Individual
财政年份：
2016
资助国家：
加拿大
起止时间：
2016-01-01 至 2017-12-31
项目状态：
已结题

来源：
https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=596780
关键词：
Aggregate Risk Completely Mixable Distributions

项目摘要

The aggregate risk is of general interest in actuarial science and quantitative risk management. An important and challenging scenario is when the individual risks have known marginal distributions but an unknown dependence structure. This scenario arises from the fact that marginal distributions can be relatively easily modeled with statistical and financial tools in practice, but the dependence structure is much more difficult to capture accurately through available data. With the dependence structure unknown, it remains difficult for the banks and insurance companies to offset the aggregated risks according to industrial regulations. Due to such a concern, researchers are trying to quantify optimal bounds on risk measures of aggregate risk. Such problems were considered extensively with various assumptions in the past few decades and they were proven to be very challenging. Recently, a new tool, called the Completely Mixable Distributions (CMD), was introduced to deal with those problems. Copulas are multivariate functions that are used to model dependence structure, which also play an important role in quantifying aggregate risk. The measures considered in this proposal include important risk quantities such as the Value-at-Risk, Conditional Tail Expectation, the variance, the expected ultility and the stop-loss premium of the aggregate risk.

总体风险是精算学和量化风险管理中普遍关注的问题。一个重要且具有挑战性的情景是，当个体风险具有已知的边际分布但具有未知的相依结构时。这种情况产生于这样一个事实，即在实践中，使用统计和金融工具可以相对容易地对边际分布进行建模，但通过现有数据准确地捕捉相关性结构要困难得多。在相关结构未知的情况下，银行和保险公司仍然很难按照行业规则来抵消聚集的风险。由于这种担忧，研究人员正试图量化总风险的风险度量的最优界限。在过去的几十年里，人们用各种假设对这些问题进行了广泛的考虑，事实证明，这些问题非常具有挑战性。最近，一种名为完全可混合分布(CMD)的新工具被引入来处理这些问题。Copula是用于对相依结构进行建模的多变量函数，它在量化总风险方面也发挥着重要作用。本方案考虑的指标包括在险价值、条件尾部期望、方差、预期效用和总风险的止损溢价等重要的风险量。