New approaches in risk measurement within advanced risk models in actuarial science

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My research program aims to investigate new approaches in risk measurement within advanced risk models in actuarial science. I will (1) propose and study non-classical ruin models which address specific situations in line with the actual management of insurance companies and (2) contribute to the study of the deep connections between ruin theory and the axiomatic framework of risk measures. The majority of existing results in ruin theory require independent increments for the process describing the aggregate claim amounts of an insurance company. There are a variety of situations where this independence assumption appears unrealistic. This is the case in presence of business cycles or delay in claim settlement. I will relax some classical assumptions within ruin models in order to account for such situations of practical relevance. On a short-term basis, I will work on ruin models dealing with underwriting cycles in the context of a large insurance company influencing the market on the one hand, and delay in claim settlement and stochastic investment on the other hand. The study of such models will enable to improve the understanding of the risks faced by an insurer and as such will contribute to a more efficient risk management of insurance companies. The concept of risk measures has become very popular in insurance, especially with the introduction of the Solvency II regulation. The Value-at-Risk risk measure has emerged as the key instrument to compute the solvency capital requirement over a one-year horizon. Although Solvency II is an improvement compared to the old insurance practices, it does not consider possible adverse situations in between or beyond the one-year horizon. The ruin theory precisely accounts for the insured risk during the whole life-time of the business or until any given time-horizons. This is why the practitioners often look at risks in the ruin context when building internal models. Risk measures derived from ruin theory will then provide more robust risk indicators. By establishing the properties (or list of axioms) of such risk measures, my research program will then provide tools to enable a better assessment of the riskiness of certain financial positions in the insurance context.