In ruin theory, an insurer’s income process is usually assumed to grow at a deterministic rate of c 0 over time. For instance, both the well-known Cramér-Lundberg risk process and the Sparre Andersen risk model have this assumption built in the construction of their respective surplus...

Conditions for the convexity of compound geometric tails and compound geometric convolution tails are established. The results are then applied to analyze the convexity of the ruin probability and the Laplace transform of the time to ruin in the classical compound Poisson risk model with and...