The Segerdahl-Tichy Process, characterized by exponential claims and state dependent drift, has drawn a considerable amount of interest, due to its economic interest (it is the simplest risk process which takes into account the effect of interest rates). It is also the simplest non-Lévy,...

As is well-known, the benefit of restricting Lévy processes without positive jumps is the “ W,Z scale functions paradigm”, by which the knowledge of the scale functions W,Z extends immediately to other risk control problems. The same is true largely for strong Markov processes X t , with...