Risk measurement and stochastic control in actuarial mathematics

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衡量问题。更准确地说，在基于随机过程的精算破产模型中，我们将研究(那些随机过程的)路径依赖泛函的概率性质，这些泛函对于偿付能力风险度量是有意义的。此外，我们还将研究与盈余过程中的现金泄漏相关的最优随机控制问题。通过这一研究计划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。

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.