Multivariate risk modeling and applications
多变量风险建模及应用
基本信息
- 批准号:RGPIN-2016-04720
- 负责人:
- 金额:$ 4.01万
- 依托单位:
- 依托单位国家:加拿大
- 项目类别:Discovery Grants Program - Individual
- 财政年份:2020
- 资助国家:加拿大
- 起止时间:2020-01-01 至 2021-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
This research program is concerned with the development of stochastic models and statistical inference procedures for the study of dependence between heterogeneous risks, particularly in situations where rare events could have disastrous economic consequences or affect public safety. This topic is of great importance, e.g., in insurance, finance or hydrology, where accounting for dependence between claims, assets or extreme precipitations is essential for responsible risk management.
Classical tools for analyzing multivariate data, e.g., regression, often rely on the unrealistic assumption that the joint distribution of the risks (or suitable transformations thereof) is normal. A more realistic approach consists of modeling the dependence between the risks directly through a copula. When dealing with continuous data, copulas allow for a separate treatment of the dependence between, and the marginal distributions of, the components of a random vector. In accordance with this goal, and to ensure that conclusions are robust to misspecification of the marginal distributions, estimators and goodness-of-fit tests for copulas are typically based on ranks.
The grant holder has been a contributor to the area since 1985 and will pursue his research along similar lines. Over the next 5 years, he will conceive and investigate new, flexible, and tractable stochastic models that are suitable for the analysis of large sets of dependent risks. To ensure that the proposed structures are easily interpretable and well adapted to risk management applications, he will focus on stochastic representations such as random scaling and common shock models. Applications to various fields will be considered. In particular, modeling techniques specifically adapted to reserve and aggregate claim processes occurring in the insurance industry will be developed. Rank-based inference techniques adapted to these models and other familiar structures exhibiting joint tail dependence, most notably Archimax copulas, will be designed using modern functional data analytic tools such as constrained B-spline smoothing. In addition, the grant holder will undertake an ambitious extension of rank-based inference techniques in order to be able to handle properly discrete, mixed, and otherwise non-continuous data using copula models. The empirical multi-linear extension copula will play a central role in these developments.
Overall, this work will help to change the manner in which statisticians, actuaries and other researchers model multivariate data. It will contribute to the growing statistical literature on high-dimensional dependence modeling and will have measurable impact in fields such as finance, insurance, hydrology, and risk management. All new methodology will be made accessible to practitioners through the R Project for Statistical Computing.
该研究计划关注的是随机模型和统计推断程序的发展,用于研究异质风险之间的依赖关系,特别是在罕见事件可能产生灾难性经济后果或影响公共安全的情况下。这个问题非常重要,例如,在保险、金融或水文领域,对索赔、资产或极端降雨之间的依赖关系进行核算对于负责任的风险管理至关重要。
用于分析多变量数据的经典工具,例如,回归,往往依赖于不切实际的假设,即联合分布的风险(或适当的转换)是正常的。一个更现实的方法是直接通过copula来建模风险之间的依赖关系。当处理连续数据时,Copula允许单独处理随机向量的分量之间的依赖性和边缘分布。根据这一目标,并确保结论是稳健的边缘分布,估计和拟合优度检验copula通常是基于秩的误设定。
赠款保持器自1985年以来一直是该领域的贡献者,并将沿着类似的方向进行研究。在接下来的5年里,他将构思和研究新的,灵活的,易于处理的随机模型,适用于大型相关风险的分析。为了确保所提出的结构易于解释,并很好地适应风险管理应用,他将专注于随机表示,如随机缩放和常见的冲击模型。将考虑各种领域的应用。特别是,建模技术,专门适用于发生在保险业的准备金和总索赔过程将被开发。基于秩的推理技术适用于这些模型和其他熟悉的结构表现出联合尾部依赖,最显着的Archimax copulas,将设计使用现代功能数据分析工具,如约束B样条平滑。此外,赠款保持器将承担一个雄心勃勃的扩展基于排名的推理技术,以便能够处理适当的离散,混合,否则不连续的数据使用copula模型。经验多线性扩展copula将在这些发展中发挥核心作用。
总的来说,这项工作将有助于改变统计学家、精算师和其他研究人员对多元数据建模的方式。它将有助于不断增长的高维依赖建模的统计文献,并将在金融,保险,水文和风险管理等领域产生可衡量的影响。所有新方法都将通过R统计计算项目向从业人员提供。
项目成果
期刊论文数量(0)
专著数量(0)
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会议论文数量(0)
专利数量(0)
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Genest, Christian其他文献
Everything you always wanted to know about copula modeling but were afraid to ask
- DOI:
10.1061/(asce)1084-0699(2007)12:4(347 - 发表时间:
2007-07-01 - 期刊:
- 影响因子:2.4
- 作者:
Genest, Christian;Favre, Anne-Catherine - 通讯作者:
Favre, Anne-Catherine
Tests of symmetry for bivariate copulas
- DOI:
10.1007/s10463-011-0337-6 - 发表时间:
2012-08-01 - 期刊:
- 影响因子:1
- 作者:
Genest, Christian;Neslehova, Johanna;Quessy, Jean-Francois - 通讯作者:
Quessy, Jean-Francois
RANK-BASED INFERENCE FOR BIVARIATE EXTREME-VALUE COPULAS
- DOI:
10.1214/08-aos672 - 发表时间:
2009-10-01 - 期刊:
- 影响因子:4.5
- 作者:
Genest, Christian;Segers, Johan - 通讯作者:
Segers, Johan
Using B-splines for nonparametric inference on bivariate extreme-value copulas
- DOI:
10.1007/s10687-014-0199-4 - 发表时间:
2014-12-01 - 期刊:
- 影响因子:1.3
- 作者:
Cormier, Eric;Genest, Christian;Neslehova, Johanna G. - 通讯作者:
Neslehova, Johanna G.
Asymptotic local efficiency of Cramer-von Mises tests for multivariate independence
- DOI:
10.1214/009053606000000984 - 发表时间:
2007-02-01 - 期刊:
- 影响因子:4.5
- 作者:
Genest, Christian;Quessy, Jean-Francois;Remillard, Bruno - 通讯作者:
Remillard, Bruno
Genest, Christian的其他文献
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{{ truncateString('Genest, Christian', 18)}}的其他基金
Stochastic Dependence Modeling
随机依赖模型
- 批准号:
CRC-2017-00051 - 财政年份:2022
- 资助金额:
$ 4.01万 - 项目类别:
Canada Research Chairs
Stochastic Dependence Modeling
随机依赖模型
- 批准号:
CRC-2017-00051 - 财政年份:2021
- 资助金额:
$ 4.01万 - 项目类别:
Canada Research Chairs
Multivariate risk modeling and applications
多变量风险建模及应用
- 批准号:
RGPIN-2016-04720 - 财政年份:2021
- 资助金额:
$ 4.01万 - 项目类别:
Discovery Grants Program - Individual
Stochastic Dependence Modeling
随机依赖模型
- 批准号:
CRC-2017-00051 - 财政年份:2020
- 资助金额:
$ 4.01万 - 项目类别:
Canada Research Chairs
Stochastic Dependence Modeling
随机依赖模型
- 批准号:
CRC-2017-00051 - 财政年份:2019
- 资助金额:
$ 4.01万 - 项目类别:
Canada Research Chairs
Multivariate risk modeling and applications
多变量风险建模及应用
- 批准号:
RGPIN-2016-04720 - 财政年份:2019
- 资助金额:
$ 4.01万 - 项目类别:
Discovery Grants Program - Individual
Stochastic Dependence Modeling
随机依赖模型
- 批准号:
CRC-2017-00051 - 财政年份:2018
- 资助金额:
$ 4.01万 - 项目类别:
Canada Research Chairs
Multivariate risk modeling and applications
多变量风险建模及应用
- 批准号:
RGPIN-2016-04720 - 财政年份:2018
- 资助金额:
$ 4.01万 - 项目类别:
Discovery Grants Program - Individual
Multivariate risk modeling and applications
多变量风险建模及应用
- 批准号:
RGPIN-2016-04720 - 财政年份:2017
- 资助金额:
$ 4.01万 - 项目类别:
Discovery Grants Program - Individual
Stochastic Dependence Modeling
随机依赖模型
- 批准号:
1000224645-2010 - 财政年份:2017
- 资助金额:
$ 4.01万 - 项目类别:
Canada Research Chairs
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