Groupe d’études et de recherche en analyse des décisions

Refracted Levy Processes

Andreas Kyprianou

We discuss solutions to a very elementary, but none the less degenerate, SDE which describes the aggregate path of a Levy process when is perturbed by a linear drift every time it spends time above a fixed level. Despite the simple nature of the SDE, some work is required to establish existence and uniqueness of a solution. This problem is put in context by an application in insurance mathematics.