Lévy processes and risk theory - Antoniadis, Ioannis; Αντωνιάδης, Ιωάννης (2023)
This thesis is dedicated to the study of Lévy processes and their applications to Risk theory. A quick and accurate recount of some prerequisites and notions is provided at the start. Following that a comprehensive study regarding the Lévy processes follows. The first part ends with the showcasing of some representative Lévy processes. In the second part, the notions of Risk theory are presented and are linked to Lévy processes via a recount of the necessary theory. Everything comes together through the inclusion of some applications utilizing real world data. Additional toy examples and simulations are included, when appropriate, in the entirety of this thesis. The thesis concludes with a brief discussion focusing on the theory and material covered, as well as, personal opinions regarding avenues for future research on Lévy processes.