Risk measurement and stochastic control in actuarial mathematics

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The last financial crisis has confirmed the importance of measuring risks. In particular, a good understanding of solvency risk is of paramount importance to reduce the negative impact of periods of financial distress. Therefore, there is a need for sophisticated mathematical models and powerful probabilistic techniques for the quantification of risks. This research program is at the interplay between the theory of stochastic processes and actuarial mathematics. Broadly speaking, its objective is to address, from a mathematical perspective, risk measurement problems faced by insurance companies. More precisely, in actuarial ruin models based on stochastic processes, we will study the probabilistic properties of path-dependent functionals (of those stochastic processes) that are of interest for solvency risk measurement. Also, we will investigate optimal stochastic control problems related to cash leakages from the surplus process. Some mathematical results obtained through this research program will be transferred to other fields of research such as actuarial finance and credit risk.