Dependence modeling and risk aggregation in actuarial science

精算科学中的依赖模型和风险聚合

• 批准号: RGPIN-2015-04057
• 负责人: Marceau, Etienne
• 金额: $ 1.46万
• 依托单位: Université Laval
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=677115
• 关键词: Dependence; modeling; risk; aggregation; actuarial

In recent years, it has become crucial for insurers and financial institutions to develop efficient risk management tools to have an appropriate assessment of the global risk associated to a portfolio which may consist of a group of insurance policies, different lines of business or different risks of an investment institution. A fair quantification of this risk must be done to insure the company's solvability. Risk theory in actuarial science aims to measure adequately this global risk, which can be examined with one-period risk models, defined over a fixed period of time. It can also be assessed with dynamic risk models by examining the behavior of the portfolio over several periods, either with discrete-time risk models or continuous-time risk models. The classical risk models propose to assess the global risk under assumptions of independence between risks and/or through time. These assumptions often lead to an inappropriate assessment of the global risk faced by insurers or investment firms. In recent years, more complex risk models which account for these dependence relations have been proposed and studied. However, much work remains to be done in this research field in order to have adequate models and tools that allow a good understanding of the global risk of a portfolio. During my last granting period, most of my research has been devoted to dependence modelling and risk aggregation within both one-period risk models and dynamic risk models. ***The long-term objective of my research program is to pursue my research on dependence modelling and risk aggregation within both one-period risk models and dynamic risk models. The realization of my research program will contribute to the development of risk modelling and to the global risk assessment under dependence assumptions.***In the forthcoming years, I will first focus on the aggregation of dependent risks, the computation of the associated risk measures, and the derivation of the contribution under capital allocation rules, assuming the following contexts: (1) the joint distribution of the dependent risks is defined through a multivariate parametric distribution; (2) the joint distribution is defined by a multivariate Archimedean copula and its marginal univariate distributions; and (3) the joint distribution is partially specified. I will also focus on the computation of ruin measures and risk measures defined in terms of ruin probabilities within discrete-time and continuous-time dynamic risk models assuming a temporal dependence. ***My research program incorporates an HQP training plan which will provide my students with scientific rigor and a strong training in actuarial risk theory, dependence modeling, aggregation of dependent risks, and capital allocation methods, which will help them either if they pursue an academic career or if they get a position in the actuarial practice, where the financial stakes can be substantial.

近年来，对于保险公司和金融机构来说，开发有效的风险管理工具以适当评估与投资组合相关的全球风险已变得至关重要，投资组合可能包括一组保单，不同的业务线或投资机构的不同风险。必须对这种风险进行公平的量化，以确保公司的可解决性。精算科学中的风险理论旨在充分衡量这种全球风险，这种风险可以用在固定时间内定义的单期风险模型进行检查。它也可以用动态风险模型来评估，通过在几个时期内检查投资组合的行为，或者用离散时间风险模型，或者用连续时间风险模型。经典风险模型建议在风险之间和/或随时间独立的假设下评估全球风险。这些假设往往导致对保险公司或投资公司所面临的全球风险的不适当评估。近年来，人们提出并研究了更复杂的风险模型来解释这些依赖关系。然而，为了有足够的模型和工具来很好地理解投资组合的全球风险，在这个研究领域还有很多工作要做。在我的上一个授权期间，我的大部分研究都是在单期风险模型和动态风险模型中进行依赖建模和风险聚合。***我的研究计划的长期目标是在单期风险模型和动态风险模型中进行依赖建模和风险聚合的研究。我的研究计划的实现将有助于风险建模的发展和依赖假设下的全球风险评估。在接下来的几年里，我将首先关注依赖风险的聚集，相关风险度量的计算，以及资本配置规则下贡献的推导，假设以下情况：(1)依赖风险的联合分布是通过多元参数分布定义的；(2)联合分布由多元阿基米德copula及其边际单变量分布定义；(3)部分确定了联合分布。我还将重点关注破产措施和风险措施的计算，这些措施是根据假定时间依赖性的离散时间和连续时间动态风险模型中的破产概率定义的。***我的研究项目包含了一个HQP培训计划，这将为我的学生提供科学的严谨性和精算风险理论、依赖模型、依赖风险汇总和资本分配方法方面的强大培训，这将有助于他们从事学术事业或在精算实践中获得一个职位，其中财务利益可能是巨大的。