Beyond the Ruin Problem: Novel applications of Insurance Risk Models

拟议的研究计划寻求在两个方面为保险和金融数学领域做出贡献。第一部分将侧重于扩展保险风险理论，特别是破产理论和风险度量方面的知识现状。然而，这种概括的方向将主要由实际应用的建模需求决定。事实上，我们研究计划的第二部分将建立在探索在保险风险理论领域发展的数学和统计技术的实际应用的基础上，特别是破产理论和意外保险建模。 几十年来，我们积累了大量的知识，现在我们在保险建模的几个领域都有了很好的理论框架。在接下来的五年里，我建议在保险风险理论提供的理解和框架下，探索在其他领域的应用。事实上，保险风险理论和意外伤害保险的发展涉及来自不同领域的工具和概念，如随机分析、统计推断、随机过程的理论和估计。在金融和保险领域，经典保险风险理论的基石以及过程和方法本身都是自然而然地产生的。我们打算探索应用的主要领域是但不限于市场微观结构和信用风险。事实上，需要研究描述这两个应用程序背后不同复杂程度的更复杂的模型。这些需求与保险风险理论和应用方面的知识很好地交织在一起，自然地产生了，也是拟议的研究计划的主题。这项研究计划试图探索围绕所谓的保险风险过程和破产问题的理论问题，方向不是由技术上的可能性和从理论观点来看的合乎逻辑的下一步决定的，而是由应用决定的。

The proposed research program seeks to contribute to the field of insurance and financial mathematics in two fronts. A first component will focus on extending the current state of knowledge in insurance risk theory, in particular in ruin theory and risk measures. However, the direction of such generalizations will be mainly dictated by the modeling needs of practical applications. Indeed, the second component of our research program will build upon the exploration of practical applications of the mathematical and statistical technology developed in the field of insurance risk theory and in particular ruin theory and casualty insurance modeling. There is a large body of knowledge that has been constructed over several decades and we now have good theoretical frameworks in several areas of insurance modeling. Over the next five years, I propose to explore applications in other fields under the lens of the understanding and framework provided by insurance risk theory. Indeed, advances in insurance risk theory and casualty insurance involve tools and concepts from different fields such as stochastic analysis, statistical inference, theory and estimation of stochastic processes. There are areas in finance and insurance where the building blocks from classical insurance risk theory, as well as the processes and methods themselves, arise naturally. The main fields where we intend to explore applications are, but not limited to, market micro-structure and credit risk. Indeed, more complex models describing the different degrees of complexity behind these two applications need to be studied. These needs intersect nicely with the body of knowledge in insurance risk theory and applications arise naturally and are the subject of the proposed research program. This research program seeks to explore theoretical questions around the so-called insurance risk processes and the ruin problem in directions that determined not by what is technically possible and a logical next step from a theoretical standpoint but they are dictated by applications.