Σεμινάριο Ελένη Βαταμίδου

ΚΥΚΛΟΣ ΣΕΜΙΝΑΡΙΩΝ ΣΤΑΤΙΣΤΙΚΗΣ ΝΟΕΜΒΡΙΟΣ 2020

Ελένη Βαταμίδου, Senior SNSF Researcher, Department of Actuarial Science, Université de Lausanne

Efficient Simulation of Ruin Probabilities When Claims are Mixtures of Heavy and Light Tails

ΠΕΡΙΛΗΨΗ

In this talk, we consider the classical Cramér-Lundberg risk model with claim sizes that are mixtures of phase-type and subexponential variables. We propose control variate techniques to efficiently simulate the ruin probability by exploiting a specific geometric compound representation. 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 illustrate numerically 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.

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