New approaches in risk measurement within advanced risk models in actuarial science

我的研究项目旨在研究精算科学中先进风险模型中风险测量的新方法。我将(1)提出并研究符合保险公司实际管理的具体情况的非经典破产模型；(2)有助于研究破产理论与风险度量的公理化框架之间的深层联系。破产理论中的大多数现有结果都需要独立的增量来描述保险公司的总索赔金额。在许多情况下，这种独立性假设似乎是不现实的。这是在存在商业周期或延迟索赔解决的情况下。我将放宽破产模型中的一些经典假设，以便解释这种实际相关的情况。在短期的基础上，我将研究破产模型，一方面在一家大型保险公司影响市场的背景下处理承保周期，另一方面在索赔结算延迟和随机投资方面。对这些模型的研究将有助于提高对保险公司面临的风险的理解，从而有助于保险公司更有效地进行风险管理。风险度量的概念在保险业已经变得非常流行，特别是随着偿付能力II法规的引入。风险价值风险度量已成为计算一年期偿付能力资本要求的关键工具。尽管偿付能力II与旧的保险实践相比有所改进，但它没有考虑一年之间或一年之后可能出现的不利情况。破产理论精确地解释了在企业的整个生命周期或直到任何给定的时间范围内的保险风险。这就是为什么从业者在构建内部模型时经常在破产环境中查看风险的原因。从破产理论衍生的风险度量将提供更可靠的风险指标。通过建立这些风险度量的属性（或公理列表），我的研究计划将提供工具，以便更好地评估保险背景下某些财务状况的风险。

My research program aims to investigate new approaches in risk measurement within advanced risk models in actuarial science. I will (1) propose and study non-classical ruin models which address specific situations in line with the actual management of insurance companies and (2) contribute to the study of the deep connections between ruin theory and the axiomatic framework of risk measures. The majority of existing results in ruin theory require independent increments for the process describing the aggregate claim amounts of an insurance company. There are a variety of situations where this independence assumption appears unrealistic. This is the case in presence of business cycles or delay in claim settlement. I will relax some classical assumptions within ruin models in order to account for such situations of practical relevance. On a short-term basis, I will work on ruin models dealing with underwriting cycles in the context of a large insurance company influencing the market on the one hand, and delay in claim settlement and stochastic investment on the other hand. The study of such models will enable to improve the understanding of the risks faced by an insurer and as such will contribute to a more efficient risk management of insurance companies. The concept of risk measures has become very popular in insurance, especially with the introduction of the Solvency II regulation. The Value-at-Risk risk measure has emerged as the key instrument to compute the solvency capital requirement over a one-year horizon. Although Solvency II is an improvement compared to the old insurance practices, it does not consider possible adverse situations in between or beyond the one-year horizon. The ruin theory precisely accounts for the insured risk during the whole life-time of the business or until any given time-horizons. This is why the practitioners often look at risks in the ruin context when building internal models. Risk measures derived from ruin theory will then provide more robust risk indicators. By establishing the properties (or list of axioms) of such risk measures, my research program will then provide tools to enable a better assessment of the riskiness of certain financial positions in the insurance context.