Risk measurement and stochastic control in actuarial mathematics

精算数学中的风险测量和随机控制

• 批准号: RGPIN-2019-06538
• 负责人: Renaud, JeanFrançois
• 金额: $ 1.46万
• 依托单位: Université du Québec à Montréal
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=738961
• 关键词: Risk; measurement; stochastic; control; actuarial

The last financial crisis has confirmed the importance of measuring risks. In particular, a good understanding of solvency risk is of paramount importance to reduce the negative impact of periods of financial distress. Therefore, there is a need for sophisticated mathematical models and powerful probabilistic techniques for the quantification of risks. This research program is at the interplay between the theory of stochastic processes and actuarial mathematics. Broadly speaking, its objective is to address, from a mathematical perspective, risk measurement problems faced by insurance companies. More precisely, in actuarial ruin models based on stochastic processes, we will study the probabilistic properties of path-dependent functionals (of those stochastic processes) that are of interest for solvency risk measurement. Also, we will investigate optimal stochastic control problems related to cash leakages from the surplus process. Some mathematical results obtained through this research program will be transferred to other fields of research such as actuarial finance and credit risk.

上一次金融危机证实了衡量风险的重要性。特别是，对偿付能力风险的良好理解对于减少财务困境时期的负面影响至关重要。因此，需要复杂的数学模型和强大的概率技术来量化风险。这个研究项目是在随机过程理论和精算数学之间的相互作用。从广义上讲，它的目标是从数学角度解决保险公司面临的风险计量问题。更确切地说，在基于随机过程的精算破产模型中，我们将研究对偿付能力风险度量感兴趣的（这些随机过程的）路径依赖泛函的概率性质。此外，我们将研究最优随机控制问题有关的现金泄漏盈余过程。通过本研究项目获得的一些数学成果将转移到其他研究领域，如精算金融和信用风险。