Beyond the Ruin Problem: Novel applications of Insurance Risk Models

超越破产问题：保险风险模型的新应用

• 批准号: RGPIN-2018-04726
• 负责人: Morales, Manuel
• 金额: $ 1.31万
• 依托单位: Université de Montréal
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=713063
• 关键词: Beyond; Ruin; Problem; Novel; applications

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.

拟议的研究计划旨在在两个方面为保险和金融数学领域做出贡献。第一个组成部分将着重于扩展保险风险理论中的当前知识状态，尤其是在毁灭理论和风险措施中。但是，这种概括的方向将主要取决于实际应用的建模需求。的确，我们研究计划的第二个组成部分将基于对保险风险理论领域（尤其是毁灭理论和伤亡保险建模领域）开发的数学和统计技术的实际应用的探索。 数十年来已经建立了许多知识，现在我们在保险建模的几个领域都拥有良好的理论框架。在接下来的五年中，我建议在保险风险理论提供的理解和框架的视角下探索其他领域的申请。确实，保险风险理论和伤亡保险的进步涉及来自不同领域的工具和概念，例如随机分析，统计推断，理论和随机过程的估计。在金融和保险中，有一些领域，可以自然出现经典保险风险理论以及过程和方法本身的构件。我们打算探索应用程序的主要领域是但不限于市场微观结构和信用风险。实际上，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的知识体系很好地相关，并且应用自然出现，并且是拟议的研究计划的主题。该研究计划旨在探讨围绕所谓的保险风险过程和方向上的毁灭问题的理论问题，这些问题不是由技术上可能做出的决定，而从理论角度来看是合乎逻辑的下一步，而是由应用程序决定的。