Analysis of an insurer surplus process and its associated ruin related quantities

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Quantification risk management is a key component of a financial toolkit developed to assist insurance companies in their aim to maintain a sound financial situation. An appropriate quantification of the risks associated with a particular block of insurance business necessitates the use of complex mathematical models that incorporate a multitude of factors that may influence (in a direct or indirect way) the claim experience of an insurance company.Over the last decade, the development of mathematical tools and the advances in computational capacity have permitted the quantitative analysis of more complex mathematical models, leading to a set of more realistic processes that are available to the insurance community to better understand the risks related to their business. Among the quantitative risk measures available, there are different quantities related to the event of ruin where ruin is defined to occur if and when the insurer has insufficient capital to meet its financial obligations. Indeed, the time at which ruin may be expected to occur, the amount of funds that may be expected to be available at the time of ruin, as well as the expected shortfall when and if ruin occurs are only few examples.My proposed research consists in examining these complex mathematical models in light of the aforementioned quantities of interest for the insurers. The mathematical concepts required to perform this analysis alluded to above are numerous and are expected to increase in number and in complexity in the future.