New approaches in loss reserving with individual models

保险人对出售给客户的合同产生的索赔负有责任，即使付款发生在合同结束后，所有保费都已收到。他必须预测支付他在法律上承诺的索赔所需的总金额，以避免破产或市场份额的损失。为了有效地执行这一任务，索赔费用的发展模式是必不可少的。传统方法侧重于描述投资组合的整体动态，而个别方法则捕捉每项索赔（或每一小组索赔）的具体动态，以便最大限度地准确预测其未来发展。拟议的研究计划旨在开发和分析涉及个人动态的新保险模型，并从微观和宏观方法对风险进行分类。第一部分是对“完工风险”的研究，即，由于保险人必须完成对保险人在各种个体模型下的活动的未决索赔的开发的缺失部分而引起的风险，量化关于个体动态的各种假设对风险水平的影响，并研究外生因素对这种风险的影响以及如何在保险公司的投资组合中控制它。第二部分专门讨论从单独和集体两种办法对风险进行比较、分类和综合。从理论的角度来看，只有一小部分关于个别模型的学术文献。解决本提案中提出的问题将通过开发一类新的模型来产生创新方法。这将有助于提高损失准备金、费率制定和再保险方面的知识。我相信，拟议的研究计划有可能转移的重点，在文献中的集体模型，这是广泛使用的风险模型，个人模型，从而提高预测的精度。从实践的角度来看，拟议的研究计划的结果将能够更准确地评估保险公司的决策对整体风险水平的影响，并将为保险公司带来更大的财务稳定性。

An insurer is liable for the claims generated by the contracts sold to clients even if payments occur after the end of the contract and all premiums have been received. He must predict the total amount necessary to pay claims that he has legally committed to cover for and to avoid insolvency or a loss of market share. To carry out this task effectively, a model for the development of claims costs is essential. In contrast to traditional approaches, which focus on describing the collective dynamics of the portfolio, individual methods capture the specific dynamics of each claim (or each small group of claims) in order to predict with maximum accuracy, their future development.*** The proposed research program aims at developing and analyzing new insurance models involving individual dynamics and to classify risks from micro- and macro-approaches. The first part is devoted to investigate the "completion risk", i.e., the risk caused by the fact that the insurer must complete the missing part of the development of an open claim on insurer's activities under various individual models, to quantify the impact of various assumptions about individual dynamics on the level of risk and to study the impact of exogenous factors on this risk and how to control it in the portfolio of an insurance company. The second part is dedicated to comparison, classification and integration of risks from both, individual and collective approaches.***From a theoretical perspective, there is only a small set of academic literature on individual models. Solving problems presented in this proposal will yield innovative approaches by developing a new class of models. This will contribute to the advancement of knowledge in loss reserving, ratemaking and reinsurance. I believe that the proposed research program has the potential of shifting the focus in the literature from collective models, which are extensively used in risk models, to individual models and thereby increase the precision of the predictions. From a practical perspective, the results of the proposed research program will enable a more accurate evaluation of the impact of insurers' decisions on the overall risk level and will lead to a greater financial stability for an insurance company.**