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

Author

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  • Hansjörg Albrecher

    (University of Lausanne)

  • Martin Bladt

    (University of Lausanne)

  • Eleni Vatamidou

    (University of Lausanne)

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.

Suggested Citation

  • Hansjörg Albrecher & Martin Bladt & Eleni Vatamidou, 2021. "Efficient Simulation of Ruin Probabilities When Claims are Mixtures of Heavy and Light Tails," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1237-1255, December.
    • Handle: RePEc:spr:metcap:v:23:y:2021:i:4:d:10.1007_s11009-020-09799-6
    DOI: 10.1007/s11009-020-09799-6
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    References listed on IDEAS

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    1. Tzougas, George & Vrontos, Spyridon & Frangos, Nicholas, 2014. "Optimal Bonus-Malus Systems Using Finite Mixture Models," ASTIN Bulletin, Cambridge University Press, vol. 44(2), pages 417-444, May.
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