Dependence modeling and risk aggregation in actuarial science

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变得至关重要，该投资组合可能包括一组保险单、不同的业务线或一家投资机构的不同风险。必须对这种风险进行合理的量化，以确保公司的偿付能力。精算学中的风险理论旨在充分衡量这种全球风险，这种风险可以通过在固定时间段内定义的一期风险模型进行检验。也可以通过检查投资组合在几个时期内的行为来使用动态风险模型进行评估，无论是使用离散时间风险模型还是使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面临的全球风险进行不恰当的评估。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，在这一研究领域仍有许多工作要做，以便有足够的模型和工具来很好地理解投资组合的全球风险。在我的上一次授予期间，我的大部分研究都致力于一期风险模型和动态风险模型中的相关性建模和风险聚合。*我的研究计划的长期目标是继续我对一期风险模型和动态风险模型中的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相关性假设下的全球风险评估。*在接下来的几年里，我将首先关注相关风险的聚合、相关风险度量的计算和资本分配规则下贡献的推导，假设以下情况：(1)依赖风险的联合分布是通过多变量参数分布定义的；(2)联合分布是由多变量阿基米德Copula及其边际单变量分布定义的；(3)联合分布是部分指定的。我还将重点讨论在假设时间相关性的离散时间和连续时间动态风险模型中，破产度量和风险度量的计算。*我的研究计划纳入了HQP培训计划，该计划将为我的学生提供科学严谨的培训，并在精算风险理论、相关性建模、相依风险聚合和资本分配方法方面进行强有力的培训，这将帮助他们追求学术生涯或在精算实践中获得一个职位，在精算实践中，财务风险可能是巨大的。

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.