We consider the classical Cram\'er-Lundberg risk model with claim sizes that
are mixtures of phase-type and subexponential variables. Exploiting a specific
geometric compound representation, we propose control variate techniques to
efficiently simulate the ruin probability in this situation. The resulting
estimators perform well for both small and large initial capital. We quantify
the variance reduction as well as the efficiency gain of our method over
another fast standard technique based on the classical Pollaczek-Khinchine
formula. We provide a numerical example to illustrate the performance, and show
that for more time-consuming conditional Monte Carlo techniques, the new series
representation also does not compare unfavorably to the one based on the
Pollaczek- Khinchine formula.Comment: 18 pages, 8 figure
