Stochastic Processes and Applications in Insurance and Finance

In actuarial mathematics, risk measurement tools are very important to reduce the negative impact of periods of financial distress.

Therefore, there is a consistent need for sophisticated mathematical and probabilistic techniques for the quantification of risks. The objective of this PhD project is to study some optimal stopping problems faced by insurance companies.

The objective is twofold: first, we study some probabilistic properties of path-dependent functionals of risk processes that are of interest for solvency risk measurement.

Second, to investigate optimal stopping and stochastic control problems related to spectrally negative Lévy processes and connected to mathematical finance.