Insurance loss model and surplus analysis

保险损失模型和盈余分析

• 批准号: RGPIN-2016-03654
• 负责人: Willmot, Gordon
• 金额: $ 2.4万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=684781
• 关键词: Insurance; loss; model; surplus; analysis

An integral part of the financial risk management activities of insurers is the accurate modelling of claims costs both at a specific juncture and over time. Such endeavors necessarily involve the use of sophisticated mathematical tools and techniques. In turn, these models are needed in order to predict and assess quantities necessary for the ongoing financial viability of the insurer. The insured public will also benefit as accurate analysis of the insurer's liabilities helps to reduce the overall costs associated with claim causing events.***One goal of the proposed research involves analysis of the so-called 'mixed Poisson' models for claim counts, and 'mixed Erlang' models for the costs of individual claim sizes. Both of these classes of models enjoy extremely useful tractable analytic and computational properties, while at the same time possessing the ability to accurately reproduce the corresponding real world insurance quantities. However, their applications in insurance, while far-reaching, are only partially understood. The proposed research will further examine their use in insurance risk management and in particular, their implications for risk related quantities such as premiums, claim liabilities, contingency reserves, etc. An important feature to be explored further with respect to mixed Poisson claim count models is their ability to accommodate risk heterogeneity of the insured population. Other useful yet less obvious consequences of their use in an insurance context will also be explored, including their ability to accommodate claims inflation (often a very costly component of claim costs), as well as their use in situations involving per claim deductibles. Similarly, mixed Erlang claim severity models are very convenient for tractable quantification of the size of losses, yet their use in situations with 'long-tailed' data inherently arising in some types of insurance has not yet been explored. Further analysis of the incorporation of dependencies between various claim sizes will also be done.***An equally important aspect of the analysis of claim costs involves their development over time, particularly in situations involving contracts of a long term nature. Historically, the somewhat distinct 'Gerber-Shiu' and 'Seal' approaches have been used. Both approaches have strengths and weaknesses insofar as the analysis of insurance solvency is concerned, and a second goal of the proposed research is to study further the uses of each of these approaches. However, it is also planned to identify and explore underlying relationships between the two approaches, thus allowing for the strengths of each approach to be carried over to the other.***The anticipated outcomes of the proposed research are more accurate and better understood modelling of the liabilities resulting from claim costs. Both insurers and the insured public will benefit financially from this additional knowledge.**

保险公司财务风险管理活动不可或缺的一部分是在特定关头和随着时间的推移时索赔成本的准确建模。这样的努力必然涉及使用复杂的数学工具和技术。反过来，为了预测和评估保险公司持续财务可行性所需的数量，需要这些模型。被保险人的公众还将受益，因为对保险公司负债的准确分析有助于降低与索赔有关的事件相关的总体成本。和“混合Erlang”模型，用于个人索赔规模的成本。这两种类别的模型都具有极为有用的可进行的分析和计算属性，同时具有准确再现相应的现实世界保险量的能力。但是，在深远的范围内，他们在保险方面的申请仅被部分理解。拟议的研究将进一步研究其在保险风险管理中的使用，尤其是它们对风险相关数量的影响，例如保费，索赔负债，应急储备等。关于混合泊松索赔模型，需要进一步探索的重要功能是他们适应被保险人口的风险异质性的能力。还将探讨其他有用但不太明显的后果，包括适应索赔通货膨胀的能力（通常是索赔成本的非常昂贵的组成部分），以及它们在涉及每个索赔扣除额的情况下的使用。同样，混合的Erlang索赔严重性模型对于损失规模的可行量化非常方便，但是在某些类型的保险中固有产生的“长尾”数据的使用中尚未探索它们的使用。还将完成对各种索赔规模之间依赖关系合并的进一步分析。从历史上看，已经使用了一些独特的“ Gerber-Shiu”和“密封”方法。就保险偿付能力的分析而言，两种方法都具有优点和缺点，而拟议研究的第二个目标是进一步研究这些方法的每种方法。但是，还计划识别和探索两种方法之间的潜在关系，从而允许将每种方法的优势传递给另一个方法。*** ***拟议研究的预期结果更准确，更好地理解了建模索赔成本造成的负债。保险公司和被保险人的公众都将从这一额外知识中受益。**