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Error Rates and Improved Algorithms for Rare Event Simulation with Heavy Weibull Tails

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  • Søren Asmussen

    (Aarhus University)

  • Dominik Kortschak

    (Université Lyon 1)

Abstract

Let Y 1,...,Y n be i.i.d. subexponential and S n = Y 1 + ⋯ + Y n . Asmussen and Kroese (Adv Appl Probab 38:545–558, 2006) suggested a simulation estimator for evaluating ${\mathbb P}(S_n>x)$ , combining an exchangeability argument with conditional Monte Carlo. The estimator was later shown by Hartinger and Kortschak (Bl DGVFM 30:363–377, 2009) to have vanishing relative error. For the Weibull and related cases, we calculate the exact error rate and suggest improved estimators. These improvements can be seen as control variate estimators, but are rather motivated by second order subexponential theory which is also at the core of the technical proofs.

Suggested Citation

  • Søren Asmussen & Dominik Kortschak, 2015. "Error Rates and Improved Algorithms for Rare Event Simulation with Heavy Weibull Tails," Methodology and Computing in Applied Probability, Springer, vol. 17(2), pages 441-461, June.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:2:d:10.1007_s11009-013-9371-6
    DOI: 10.1007/s11009-013-9371-6
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    References listed on IDEAS

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    1. Asmussen, S. & Binswanger, K., 1997. "Simulation of Ruin Probabilities for Subexponential Claims," ASTIN Bulletin, Cambridge University Press, vol. 27(2), pages 297-318, November.
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    Cited by:

    1. Søren Asmussen & Jaakko Lehtomaa, 2017. "Distinguishing Log-Concavity from Heavy Tails," Risks, MDPI, vol. 5(1), pages 1-14, February.
    2. O. J. Boxma & E. J. Cahen & D. Koops & M. Mandjes, 2019. "Linear Stochastic Fluid Networks: Rare-Event Simulation and Markov Modulation," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 125-153, March.
    3. 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.

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