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。后者可以用固定时间段内的短期风险模型来检验。它也可以通过检查投资组合在几个时期内的行为来评估长期动态风险模型，无论是离散时间风险模型还是连续时间风险模型。很明显，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、更复杂的模型来解释风险之间和/或时间上的依赖关系。这些改进需要新的办法和方法来适当量化全球风险。在过去的六年里，我的研究主要集中在短期风险模型、连续时间风险模型和离散时间相依风险模型。我目前和长期的目标是从事精算学中具有依赖性的风险模型的研究。短期目标是：（1）提出短期风险模型中的相关结构，开发聚合方法，以评估所提出模型中的风险措施并确定资本分配;（2）提出了具有相依性的连续时间和离散时间风险模型，给出了破产测度的估计，并对离散时间和连续时间相依风险模型中的风险量（如贴现总索赔额）进行了估计。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测量和量化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.