Risk models with dependence in actuarial science/ Modèles de risque avec dépendance en sciences actuarielles

对投资组合的全球风险进行适当的评估对保险公司或投资公司来说至关重要。在精算学中，风险理论的主要目标是评估这种全球风险。后者可以在一段固定的时间内用短期风险模型进行检验。它也可以用长期动态风险模型来评估，方法是检查投资组合在几个时期内的行为，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。显然，传统上基于独立性假设的风险模型低估或高估了全球风险。需要更好、更复杂的模型来考虑风险之间和/或时间上的相关性。这些改进需要新的途径和方法来适当地量化全球风险。在过去的六年里，我的大部分研究都致力于短期风险模型、连续时间风险模型和具有相依关系的离散时间风险模型。我目前和长期的目标是继续研究精算学中具有相关性的风险模型。短期目标是：(1)提出短期风险模型中的相依性结构，发展聚集方法以评估所建议模型中的风险度量并确定资本分配；(2)提出具有相依性的连续时间和离散时间风险模型，评估破产度量，以及评估离散时间和连续时间相依风险模型中的风险量(如贴现的总索赔额)。从长远来看，我的研究计划的实现将为精算师提供新的工具，使他们能够在可能依赖的假设下衡量和鉴定风险组合的全球风险。

An appropriate assessment of the global risk of a portfolio is crucial for an insurance company or an investment firm. In actuarial science, the main objective of risk theory is to evaluate this global risk. The latter can be examined with short term risk models over a fixed period of time. It can also be assessed with long term dynamic risk models by examining the behaviour of the portfolio over several periods, either with discrete-time risk models or continuous-time risk models. It is clear that risk models traditionally based on the independence assumption underestimate or overestimate the global risk. Better, more complex models are needed to account for dependence among risks and/or through time. These improvements require new approaches and methods to quantify appropriately the global risk. During the last six years, most of my research has been devoted to short term risk models, continuous-time risk models and discrete-time risk models with dependence. My present and long-term objective is to pursue the study of risk models with dependence in actuarial science. The short-term objectives are: (1) To propose dependence structures in short term risk models, to develop aggregation methods in order to evaluate risk measures within the proposed models and to determine the capital allocation; (2) To propose continuous-time and discrete-time risk models with dependence, to evaluate ruin measures, and to evaluate the risk quantities (such as the discounted aggregate claim amount) in discrete-time and continuous-time risk models with dependence. In the long run, the realization of my research program will provide new tools to actuaries, enabling them to measure and qualify the global risk of a portfolio of risks under the assumption of possible dependence.