Dependence in actuarial science: multivariate models, risk assessment and claim reserving

自20世纪90年代开始，允许依赖关系的精算模型的构建已经取得了进展，它们在不同背景下的应用已经证明了它们的有用性。尽管如此，工业中的问题仍未得到解决，需要更合适的依赖结构以及评估感兴趣数量的数值工具。基于依赖结构的风险模型一直是风险理论和损失准备金等领域的研究热点。仍然需要进一步发展，以提供更灵活和适当的依赖框架，以及必要的有效数值方法，以充分量化这种情况下的风险。***我在未来几年的研究计划包括在风险理论和损失保留设置中发展新的多元框架，并使用数值工具在这些框架内准确或数值地评估风险。这些创新将更适合现代精算师的任务。在短期内，我将提出新的方法来构建风险投资组合的双变量和多变量模型，并研究在这些模型下的风险聚集和资本配置。为此，我将在大型投资组合的背景下提出有效的数值和抽样方法来计算依赖损失函数的风险度量。这些结构和工具将用于提出多期风险模型——基于依赖假设的模型和多个业务线的模型。这种动态风险模型允许随着时间的推移评估与投资组合相关的风险。将提出和研究损失准备金的多变量结构，以充分评估与保险公司活动相关的整体风险，而不仅仅是针对每个风险类别。准备金是金融机构财务报表的重要组成部分，为将来的索偿款项设定适当的准备金水平是财产/意外保险精算师的主要任务之一。***从长远来看，我的研究计划中所解决的问题将使精算师更好地了解他们承担的风险和确保其运营所需的资本数量。该计划通过研究和培训主张进行创新，这些主张是保险公司活动的核心，影响其在行业中的地位和财务实力。＊＊＊＊＊

The construction of actuarial models allowing dependence relationships has progressed since its beginning in the 1990's and their application in different contexts has demonstrated their usefulness. Nonetheless, problems in industry remain unsolved and more suitable dependence structures as well as numerical tools to evaluate quantities of interest are needed. Risk models based on dependence structures are still at the center of ongoing research in different areas such as risk theory and loss reserving. Further developments are still required to provide more flexible and suitable dependence frameworks with the necessary efficient numerical methods to adequately quantify risks in such contexts.***My research program over the next few years consists in developing in risk theory and loss reserving settings new multivariate frameworks with numerical tools to evaluate risks exactly or numerically within such frameworks. These innovations will be better suited for modern tasks of actuaries. In the short term, I will propose new approaches to construct bivariate and multivariate models for risk portfolios and examine risk aggregation and capital allocation under them. To this aim, I will propose in the context of large portfolios efficient numerical and sampling methods to compute risk measures for functions of dependent losses. These constructions and tools will be used to propose multiperiod risk models models under dependence assumptions and for several lines of business. Such dynamic risk models allow evaluating the risks associated to a portfolio over time. Multivariate constructions will be proposed and studied for loss reserving to appraise adequately the risks associated to the activities of insurance companies as a whole and not solely for each risk class. Reserves consist of a major element in financial statements of a financial institution and setting an appropriate reserve level for future claims payment is one of the main tasks of property/casualty actuaries.***In the long term, the questions addressed in my research program will enable actuaries to have a better understanding of the risks they undertake and the needed amount of capital to secure their operations. This program innovates with research and training propositions that are at the core of the activities of an insurance company which impact their position in the industry and financial strength. *****