New approaches in loss reserving with individual models

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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.**