Modelling, Quantifying and Managing Risk in Insurance and Related Areas

保险是一项冒险业务，这使得建模、量化和管理风险对任何保险组织的成功至关重要。计算技术的进步和定量方法的成熟意味着精算科学中定量模型的使用显著增加。我提出的研究将涉及一般保险的几个领域的保险风险问题，如随机索赔准备金、定价和保险风险理论。我提出的模型和方法将在操作风险和相关领域进行探讨。在随机索赔准备金中，我将探索预测财产和意外伤害保险中发生的已报告但未结算（RBNS）准备金和已发生但未报告（IBNR）准备金的方法，这是保险公司资产负债表中最重要的组成部分。特别是，我计划研究标记Cox过程的使用及其推广。在各种隐马尔可夫模型假设下使用混合专家分布将是我们保留或可信度类型技术的核心。我将开发期望最大化类型的算法来拟合模型参数，这些参数可能允许包含协变量信息。报告延迟、结算延迟和索赔规模之间的依赖结构将通过参数分布和非参数分布、copula和部分指定的联合分布来详细考虑。第二阶段的研究将基于保险风险理论方面的工作。与我的团队一起，我将专注于评估与保险业务相关的全球风险，试图评估偿付能力要求。为此，我将用更现实、更复杂的风险模型取代经典的泊松、更新和马尔可夫风险模型。我的新模型将能够考虑更一般的点流程，可以解释报告和结算延迟以及与事故事件相关的多重支付。我将主要关注考虑通过频率、严重程度和资本注入引入的各种依赖结构的多变量风险模型。风险的量化和管理将通过破产相关措施来确定，这些措施可能会解释那些在估值时间之前未报告或未结算的事件的准备金。我希望我的研究成果能够对保险行业产生实质性的长期影响。我预计本提案中开发的模型、方法和数值程序将特别引起精算师的兴趣，因为我正在从事的项目来自保险行业。此外，这些方法将被适应并应用于其他领域，如管理操作风险。

Insurance is a risk-taking business, which makes modelling, quantifying, and managing risk crucial to the success of any insurance organization. Advances in computing technology and the maturing of quantitative methods have meant a significant increase in the use of quantitative models in actuarial science. My proposed research will address insurance risk problems in several areas of general insurance, such as stochastic claim reserving, pricing, and insurance risk theory. The models and methods I propose will be explored in operational risk and related areas. In stochastic claim reserving, I will explore ways to predict the Reported But Not Settled (RBNS) reserve and the Incurred But Not Reported (IBNR) reserve that occur in Property and Casualty Insurance - among the most important components of an insurance company's balance sheet. In particular, I plan to investigate the use of marked Cox processes and their generalizations. The use of mixture of experts distributions under various Hidden Markov Model assumptions will be at the core of our reserving or credibility type techniques. I will develop Expectation Maximization type algorithms for fitting the model parameters that will possibly allow for the inclusion of covariate information. The dependence structures among reporting delays, settlement delays, and claim sizes will be considered in detail via parametric and non-parametric distributions, copulas, and partially specified joint distributions. A second stage of the research will be based on work in insurance risk theory. With my team, I will focus on the assessment of global risk associated with the insurance business in an attempt to evaluate solvency requirements. To this end, I will replace the classical Poisson, renewal, and Markovian type risk models with more realistic and sophisticated ones. My new models will be able to consider more general point processes that can account for reporting and settlement delays and for multiple payments associated with the accident events. I will mainly focus on multivariate risk models that consider various dependence structures introduced via frequencies, severities, and capital infusions. The quantification and management of risk will be determined via ruin related measures that will account potentially for reserves for those events that are not reported or not settled prior to the valuation time. I expect my research results to have a substantial long-term impact on the insurance industry. I anticipate that the models, methodologies, and numerical procedures developed in this proposal will especially interest actuaries, as the projects I am working on come from the insurance industry. Moreover, these methods will be adapted and applied to other areas such as managing operational risk.