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Simulation of Ruin Probabilities for Subexponential Claims

Author

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  • Asmussen, S.
  • Binswanger, K.

Abstract

We consider the classical risk model with subexponential claim size distribution. Three methods are presented to simulate the probability of ultimate ruin and we investigate their asymptotic efficiency. One, based upon a conditional Monte Carlo idea involving the order statistics, is shown to be asymptotically efficient in a certain sense. We use the simulation methods to study the accuracy of the standard Embrechts-Veraverbeke [16] approximation for the ruin probability and also suggest a new one based upon ideas of Hogan [21].

Suggested Citation

  • Asmussen, S. & Binswanger, K., 1997. "Simulation of Ruin Probabilities for Subexponential Claims," ASTIN Bulletin, Cambridge University Press, vol. 27(2), pages 297-318, November.
    • Handle: RePEc:cup:astinb:v:27:y:1997:i:02:p:297-318_01
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    Cited by:

    1. Fabian Dickmann & Nikolaus Schweizer, 2014. "Faster Comparison of Stopping Times by Nested Conditional Monte Carlo," Papers 1402.0243, arXiv.org.
    2. Zdravko I. Botev & Robert Salomone & Daniel Mackinlay, 2019. "Fast and accurate computation of the distribution of sums of dependent log-normals," Annals of Operations Research, Springer, vol. 280(1), pages 19-46, September.
    3. Albrecher Hansjörg & Kantor Josef, 2002. "Simulation of ruin probabilities for risk processes of Markovian type," Monte Carlo Methods and Applications, De Gruyter, vol. 8(2), pages 111-128, December.
    4. Sandeep Juneja, 2001. "Importance Sampling and the Cyclic Approach," Operations Research, INFORMS, vol. 49(6), pages 900-912, December.
    5. Luis Rincón & David J. Santana, 2022. "Ruin Probability for Finite Erlang Mixture Claims Via Recurrence Sequences," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 2213-2236, September.
    6. Coulibaly, Ibrahim & Lefèvre, Claude, 2008. "On a simple quasi-Monte Carlo approach for classical ultimate ruin probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 935-942, June.
    7. Martire, Antonio Luciano, 2022. "Volterra integral equations: An approach based on Lipschitz-continuity," Applied Mathematics and Computation, Elsevier, vol. 435(C).
    8. Dassios, Angelos & Jang, Jiwook & Zhao, Hongbiao, 2015. "A risk model with renewal shot-noise Cox process," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 55-65.
    9. Paulsen, Jostein & Kasozi, Juma & Steigen, Andreas, 2005. "A numerical method to find the probability of ultimate ruin in the classical risk model with stochastic return on investments," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 399-420, June.
    10. Joshua Chan & Dirk Kroese, 2011. "Rare-event probability estimation with conditional Monte Carlo," Annals of Operations Research, Springer, vol. 189(1), pages 43-61, September.
    11. Dassios, Angelos & Jang, Jiwook & Zhao, Hongbiao, 2015. "A risk model with renewal shot-noise Cox process," LSE Research Online Documents on Economics 64051, London School of Economics and Political Science, LSE Library.
    12. Tamturk, Muhsin & Utev, Sergey, 2018. "Ruin probability via Quantum Mechanics Approach," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 69-74.
    13. Hélène Cossette & Etienne Marceau & Quang Huy Nguyen & Christian Y. Robert, 2019. "Tail Approximations for Sums of Dependent Regularly Varying Random Variables Under Archimedean Copula Models," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 461-490, June.
    14. Nam Kyoo Boots & Perwez Shahabuddin, 2001. "Simulating Tail Probabilities in GI/GI.1 Queues and Insurance Risk Processes with Subexponentail Distributions," Tinbergen Institute Discussion Papers 01-012/4, Tinbergen Institute.
    15. 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.
    16. David J. Santana & Juan González-Hernández & Luis Rincón, 2017. "Approximation of the Ultimate Ruin Probability in the Classical Risk Model Using Erlang Mixtures," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 775-798, September.
    17. Karthyek R. A. Murthy & Sandeep Juneja & Jose Blanchet, 2012. "State-independent Importance Sampling for Random Walks with Regularly Varying Increments," Papers 1206.3390, arXiv.org, revised Sep 2014.
    18. Yuguang Fan & Philip S. Griffin & Ross Maller & Alexander Szimayer & Tiandong Wang, 2017. "The Effects of Largest Claim and Excess of Loss Reinsurance on a Company’s Ruin Time and Valuation," Risks, MDPI, vol. 5(1), pages 1-27, January.
    19. Søren Asmussen & Reuven Y. Rubinstein, 1999. "Sensitivity Analysis of Insurance Risk Models via Simulation," Management Science, INFORMS, vol. 45(8), pages 1125-1141, August.

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