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: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=668660
• 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的一个组成部分是对特定时刻和一段时间内的索赔成本进行准确建模。这些努力必然涉及复杂的数学工具和技术的使用。反过来，需要这些模型来预测和评估保险公司持续财务生存所需的数量。受保公众也将受益，因为对保险公司负债的准确分析有助于降低与索赔事件相关的总体成本。***拟议研究的一个目标是分析所谓的索赔计数“混合泊松”模型，以及针对单个索赔金额的成本的“混合 Erlang”模型。这两类模型都具有极其有用的易于处理的分析和计算特性，同时具有准确再现相应的现实世界保险金额的能力。然而，它们在保险领域的应用虽然影响深远，但人们对它们的了解却只有部分。拟议的研究将进一步检验它们在保险风险管理中的应用，特别是它们对风险相关量（如保费、索赔责任、应急准备金等）的影响。混合泊松索赔计数模型有待进一步探索的一个重要特征是他们适应受保人群风险异质性的能力。还将探讨它们在保险领域中使用的其他有用但不太明显的后果，包括它们适应索赔膨胀的能力（通常是索赔成本中非常昂贵的组成部分），以及它们在涉及每项索赔免赔额的情况下的使用。同样，混合 Erlang 索赔严重程度模型对于损失规模的易于处理的量化非常方便，但尚未探索在某些类型的保险中固有地产生“长尾”数据的情况下使用它们。还将对各种索赔规模之间的依赖性进行进一步分析。***索赔成本分析的一个同样重要的方面涉及索赔成本随时间的发展，特别是在涉及长期合同的情况下。从历史上看，使用了有些不同的“Gerber-Shiu”和“Seal”方法。就保险偿付能力分析而言，这两种方法各有优缺点，本研究的第二个目标是进一步研究每种方法的用途。然而，还计划识别和探索两种方法之间的潜在关系，从而将每种方法的优势转移到另一种方法上。***拟议研究的预期结果是更准确和更好理解的建模索赔费用产生的负债。保险公司和受保公众都将从这些额外的知识中获得经济利益。**