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。精算学中的风险理论旨在充分衡量这种全球风险，这可以通过在固定时间段内定义的单期风险模型进行检查。它也可以通过动态风险模型来评估，通过检查投资组合在几个时期内的行为，无论是离散时间风险模型还是连续时间风险模型。经典的风险模型建议在风险之间和/或通过时间独立的假设下评估全局风险。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，更复杂的风险模型，占这些依赖关系已被提出和研究。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，使人们能够很好地了解投资组合的全球风险。在我的最后一个授予期间，我的大部分研究一直致力于单期风险模型和动态风险模型中的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相关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，我将首先关注相关风险的聚集，相关风险度量的计算，以及资本分配规则下贡献的推导，假设以下情况：（1）相关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）联合分布是部分指定的。我也将专注于破产措施和风险措施的计算破产概率定义在离散时间和连续时间的动态风险模型假设时间依赖。* 我的研究计划包括一个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，依赖建模，依赖风险聚合和资本配置方法的强大培训，这将有助于他们无论是追求学术生涯还是如果他们在精算实践中获得一个职位，其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.