Analysis of the insurer's surplus and related quantities

健全的财务风险管理要求保险公司审查在某一特定保险业务块上发生不利索赔的可能性。这种审查的性质需要使用详细的数学模型来提供对该业务潜在索赔经验的看法。特别是，应用概率的技术可以用于量化“破产”发生的可能性，即保险公司在任何时刻都没有足够的资金来满足这些索赔责任。此外，这种方法也可以用来洞察导致毁灭的事件的本质。在过去的十年里，数学上的进步使人们能够系统地定量分析破产可能发生的时间，当破产发生时，保险公司可以用来支付索赔的资金，导致破产发生的索赔的性质，以及保险公司面临的最终短缺。此外，现在有了强大的计算资源，可以使用更现实的数学模型，而这些模型必然比以前考虑的更复杂。拟议研究的目的是检查这些复杂的模型，以检查保险公司的资金导致破产的分析和这种破产本身的性质。鉴于现在可用的各种各样的数学工具，这种分析现在看来是可能的。

Sound financial risk management requires that the insurer examine the possibility of adverse claims experience on a given block of insurance business. The nature of such examination necessitates the use of detailed mathematical models to provide a view of the potential claims experience of this business. In particular, techniques from applied probability may be applied to quantify the possibility that 'ruin' occurs, i.e. that the insurer has insufficient capital to meet these claim liabilities at any juncture. Furthermore, this approach may also be used to provide insight into the nature of the events leading up to ruin. Mathematical advances in the last decade have allowed for a systematic quantitative analysis of the time at which ruin may be expected to occur, the funds which are available to the insurer for claims payments when this happens, the nature of the claims which cause this to happen, and the resultant shortfall faced by the insurer. Moreover, powerful computational resources are now available which permit the use of more realistic mathematical models which are of necessity more complex than those previously considered. The purpose of the proposed research is to examine such complex models with a view to the examination of the analysis of the insurer's funds leading up to ruin and the nature of such ruin itself. Such analysis now appears to be possible in light of the wide variety of mathematical tools which are now available.