Modeling Individual Trajectories in Loss Reserving

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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.