Dependence in risk theory

风险理论中的依赖性

• 批准号: 194353-2007
• 负责人: Cossette, Hélène
• 金额: $ 1.24万
• 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: 2011
• 资助国家: 加拿大
• 起止时间: 2011-01-01 至 2012-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=476652
• 关键词: Dependence; risk; theory

An insurance company submits itself to an important risk by subscribing a high number of insurance policies. To avoid facing financial difficulties in the future, insurance companies must be able to have an adequate appraisal of the financial health of their institution. For that purpose, risk theory can be used to measure the global risk of a portfolio of insurance contracts. This evaluation can be made with short term models over a fixed period of time and with long term models. With long term models, the global risk can be assessed by examining the evolution of the surplus process over several periods, either on a discrete or continuous time basis. In such a case, ruin theory is most oftenly used to accomplish this task. The description of the characteristics of the surplus process has relied traditionally on an assumption of independence between the amount of claims and the interarrival times. In many applications, this assumption is inadequate and generalizations with a dependence structure is needed to avoid a misevaluation of the global risk faced by an insurance company. In my research program, I will propose and include different dependence constructions which can be observed in practice in risk models. Both discrete and continuous time risk models will be considered. Different quantities such as the ruin probability, the surplus immediately prior to ruin and the deficit at ruin are of interest in the assessment of the risk of an insurance portfolio. The unified approach based on the Gerber-Shiu penalty function will be used to study these ruin related quantities in the extensions proposed. The possibility of dividend payments to shareholders and investment income will also be studied within the suggested risk models with dependence.

一家保险公司通过订购大量的保险单来承担重大风险。为了避免将来面临财务困难，保险公司必须能够对其机构的财务状况进行充分的评估。为此，风险理论可以用来衡量保险合同组合的整体风险。这种评估可以使用固定时间段内的短期模型和长期模型进行。对于长期模型，可以通过在离散或连续时间基础上检查盈余过程在几个时期内的演变来评估全球风险。在这种情况下，破产理论是最经常用来完成这项任务。盈余过程的特征的描述传统上依赖于索赔额和到达间隔时间之间的独立性的假设。在许多应用中，这种假设是不充分的，需要用依赖结构进行概括，以避免对保险公司面临的全球风险进行错误评估。在我的研究计划中，我将提出并包括在风险模型中可以在实践中观察到的不同依赖结构。将考虑离散和连续时间风险模型。不同的量，如破产概率，破产前的盈余和破产时的赤字是在评估的保险组合的风险感兴趣。 基于Gerber-Shiu罚函数的统一方法将用于研究所提出的扩展中的这些破产相关量。还将在建议的具有相关性的风险模型中研究向股东支付股息和投资收入的可能性。