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

Hansjörg Albrecher (), Martin Bladt () and Eleni Vatamidou ()
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Hansjörg Albrecher: University of Lausanne
Martin Bladt: University of Lausanne
Eleni Vatamidou: University of Lausanne

Methodology and Computing in Applied Probability, 2021, vol. 23, issue 4, 1237-1255

Abstract: Abstract We consider the classical Cramér-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.

Keywords: Rare event simulation; Ruin probability; Cramér-Lundberg model; Insurance risk theory; 65C06 (60G50; 62P05; 65C50) (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11009-020-09799-6

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