Dependence in actuarial science: multivariate models, risk assessment and claim reserving

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The construction of actuarial models allowing dependence relationships has progressed since its beginning in the 1990's and their application in different contexts has demonstrated their usefulness. Nonetheless, problems in industry remain unsolved and more suitable dependence structures as well as numerical tools to evaluate quantities of interest are needed. Risk models based on dependence structures are still at the center of ongoing research in different areas such as risk theory and loss reserving. Further developments are still required to provide more flexible and suitable dependence frameworks with the necessary efficient numerical methods to adequately quantify risks in such contexts.***My research program over the next few years consists in developing in risk theory and loss reserving settings new multivariate frameworks with numerical tools to evaluate risks exactly or numerically within such frameworks. These innovations will be better suited for modern tasks of actuaries. In the short term, I will propose new approaches to construct bivariate and multivariate models for risk portfolios and examine risk aggregation and capital allocation under them. To this aim, I will propose in the context of large portfolios efficient numerical and sampling methods to compute risk measures for functions of dependent losses. These constructions and tools will be used to propose multiperiod risk models models under dependence assumptions and for several lines of business. Such dynamic risk models allow evaluating the risks associated to a portfolio over time. Multivariate constructions will be proposed and studied for loss reserving to appraise adequately the risks associated to the activities of insurance companies as a whole and not solely for each risk class. Reserves consist of a major element in financial statements of a financial institution and setting an appropriate reserve level for future claims payment is one of the main tasks of property/casualty actuaries.***In the long term, the questions addressed in my research program will enable actuaries to have a better understanding of the risks they undertake and the needed amount of capital to secure their operations. This program innovates with research and training propositions that are at the core of the activities of an insurance company which impact their position in the industry and financial strength. *****