Analysis of an insurer surplus process and its associated ruin related quantities

量化风险管理是一套金融工具的关键组成部分，旨在帮助保险公司实现维持稳健财务状况的目标。要对与某一特定保险业务相关的风险进行适当量化，就必须使用复杂的数学模型，其中包含可能（直接或间接地）影响保险公司索赔经验的众多因素。在过去的十年中，数学工具的发展和计算能力的进步已经允许对更复杂的数学模型进行定量分析，从而导致一组更现实的过程，可供保险社区更好地了解与其业务相关的风险。在可用的定量风险度量中，有不同的与破产事件相关的数量，其中破产被定义为当保险公司没有足够的资金来履行其财务义务时发生。实际上，破产可能发生的时间，破产时可能可用的资金数量，以及破产发生时和如果发生破产时的预期短缺只是几个例子。我建议的研究包括根据上述保险公司的利益数量来检查这些复杂的数学模型。执行上述分析所需的数学概念很多，并且预计将来在数量和复杂性上都将增加。

Quantification risk management is a key component of a financial toolkit developed to assist insurance companies in their aim to maintain a sound financial situation. An appropriate quantification of the risks associated with a particular block of insurance business necessitates the use of complex mathematical models that incorporate a multitude of factors that may influence (in a direct or indirect way) the claim experience of an insurance company.Over the last decade, the development of mathematical tools and the advances in computational capacity have permitted the quantitative analysis of more complex mathematical models, leading to a set of more realistic processes that are available to the insurance community to better understand the risks related to their business. Among the quantitative risk measures available, there are different quantities related to the event of ruin where ruin is defined to occur if and when the insurer has insufficient capital to meet its financial obligations. Indeed, the time at which ruin may be expected to occur, the amount of funds that may be expected to be available at the time of ruin, as well as the expected shortfall when and if ruin occurs are only few examples.My proposed research consists in examining these complex mathematical models in light of the aforementioned quantities of interest for the insurers. The mathematical concepts required to perform this analysis alluded to above are numerous and are expected to increase in number and in complexity in the future.