Actuarial risk models with dependence

具有依赖性的精算风险模型

• 批准号: 194353-2012
• 负责人: Cossette, Hélène
• 金额: $ 1.09万
• 依托单位: Université Laval
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=593698
• 关键词: Actuarial; risk; models; dependence

For an insurance company or an investment firm, it is of utmost importance to make an adequate assessment of the global risk of a portfolio which can be 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. 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 must still be accomplished in this young research field in order to have adequate models and tools that allow a good understanding of the global risk of a portfolio. With my research program, I will contribute to the development of short term and long term risk modelling and global risk assessment under dependence assumptions. More precisely, I will derive aggregation methods, analyze risk measures and capital allocation within portfolios with dependent risks. I will also analyze risk and ruin measures within three types of continuous-time risk models: earthquake models, risk models with general dependence structure between interclaim times and losses, and dependent Sparre-Andersen risk models with interest. Finally, I will analyze risk and ruin measures within discrete-time risk models with three different forms of dependence structure: temporal dependence, random income, and correlated classes of business.

对于保险公司或投资公司来说，对投资组合的全球风险进行充分评估是至关重要的，投资组合可以是一组保单，不同的业务范围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。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，在这个年轻的研究领域，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。通过我的研究项目，我将为短期和长期风险建模以及依赖假设下的全球风险评估的发展做出贡献。更确切地说，我将推导出聚合方法，分析风险度量和具有相关风险的投资组合中的资本配置。我还将分析三种类型的连续时间风险模型中的风险和破产措施：地震模型，索赔时间和损失之间具有一般相关结构的风险模型，以及具有利息的相关Sparre-Andersen风险模型。最后，我将分析具有三种不同形式的依赖结构的离散时间风险模型中的风险和破产度量：时间依赖，随机收入和相关业务类别。