Modeling Individual Trajectories in Loss Reserving

当保险公司与客户签订合同时，它通常承诺承保一定期间内发生的所有索赔。对于非人寿保险产品（例如汽车或火灾保险），索赔有时会在一段时间后报告给保险公司，然后在较短或较长的时间后支付。为了保护所有保单持有人，法律通过会计准则和财务报告来规范保险公司的财务管理。更具体地说，在加拿大，金融机构监督办公室制定了关于保险公司偿付能力的指导方针，并确定了在任何时候都需要可用的最低资本数额，以应对保险风险。按照这些指导方针，有必要预测未来将为投资组合中的每一项索赔支付的金额和时间（索赔的轨迹或路径）。然后，就有可能评估投资组合的风险，并建立我们所说的“储备”。长期以来，这个问题一直是使用汇总数据来解决的，但近年来，个人（或微观层面）的方法被提出，为一个新的研究领域打开了大门。本研究计划的长期总体目标是详细阐述和调查考虑到索赔特定特征的非寿险产品的个别模型。为了实现这一目标，研究将沿着下面总结的两条主线进行。1. 风险评估过程中轨迹内依赖性和轨迹间依赖性的建模。这种依赖可能是由几个人驾驶同一辆车或与同一汽车保险合同相关的几个保险范围（碰撞，直接赔偿财产损失等）引起的。2. 制定有效的个人非寿险损失准备金方法。例如，考虑个人轨迹的早期阶段，以区分不寻常的文件，即公司必须特别注意的文件，这可能意味着时间和成本，以及通常的文件。对于精算研究人员来说，所获得的结果将为探索新的研究提供新的、更准确的模型：风险分析与管理、算法等。此外，其影响将是通过使公司更好地了解和管理投资组合中的风险，为保单持有人提供更大的保护。虽然研究结果的主要影响将在保险公司偿付能力评估领域，但预计将有更广泛的应用，主要是在费率制定过程和再保险方面。

When an insurance company concludes a contract with a client, it generally undertakes to cover all claims that occur during a specified period. For a non-life insurance product (e.g. car or fire insurance), claims are reported to the insurer, sometimes after some delay, and then paid after a shorter or longer period of time. To protect all policyholders, laws exist to regulate the financial management of an insurance company through accounting standards and financial reporting. More specifically, in Canada, the Office of the Superintendent of Financial Institutions sets guidelines with regard to the solvency of the insurer and defines a minimum amount of capital that needs to be available at all times to address insurance risks. Following these guidelines, it is necessary to predict the amount and the moment of each of the payments that will be made in the future, for each of the claims in the portfolio (the trajectory, or the path, of the claim). Then, it is possible to evaluate the risk of a portfolio and to establish what we call "reserves". This problem has long been approached using aggregated data but in recent years, individual (or micro-level) approaches have been proposed, opening the door to a new field of research. The long-term overall objective of this research program is to elaborate and investigate individual models for non-life insurance products that take into account claim-specific characteristics. To achieve this, the research will be conducted along two main lines summarized below. 1. Modeling within- and between-trajectories dependence in the risk evaluation process.  This dependence can be caused by several people driving the same vehicle or several coverages (collision, direct compensation for property damage, etc.) associated with the same automobile insurance contract. 2. Elaborating efficient individual approaches in non-life loss reserving. For example, considering the early stage of an individual trajectory to distinguish between unusual files, i.e., files in which the company will have to pay special attention, with the time and costs that this may imply, and usual files. For researchers in actuarial science, the results obtained will provide new and more accurate models on which to explore new research: risk analysis and management, algorithms, etc. Moreover, the impact will be to provide greater protection for policyholders by enabling companies to better understand and manage the risks in a portfolio. Although the main impacts of the results will be in the field of the evaluation of insurance companies' solvency, more extensive applications are to be expected, mainly in the ratemaking process and reinsurance.