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Computation of Compound Distributions I: Aliasing Errors and Exponential Tilting

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  • Grübel, Rudolf
  • Hermesmeier, Renate

Abstract

Numerical evaluation of compound distributions is one of the central numerical tasks in insurance mathematics. Two widely used techniques are Panjer recursion and transform methods. Many authors have pointed out that aliasing errors imply the need to consider the whole distribution if transform methods are used, a potential drawback especially for heavy-tailed distributions. We investigate the magnitude of aliasing errors and show that this problem can be solved by a suitable change of measure.

Suggested Citation

  • Grübel, Rudolf & Hermesmeier, Renate, 1999. "Computation of Compound Distributions I: Aliasing Errors and Exponential Tilting," ASTIN Bulletin, Cambridge University Press, vol. 29(2), pages 197-214, November.
    • Handle: RePEc:cup:astinb:v:29:y:1999:i:02:p:197-214_01
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    Citations

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    Cited by:

    1. Xiaolin Luo & Pavel V. Shevchenko, 2009. "Computing Tails of Compound Distributions Using Direct Numerical Integration," Papers 0904.0830, arXiv.org, revised Feb 2010.
    2. Lorenzo Cappello & Stephen G. Walker, 2018. "A Bayesian Motivated Laplace Inversion for Multivariate Probability Distributions," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 777-797, June.
    3. Dominique Guegan & Bertrand Hassani, 2009. "A modified Panjer algorithm for operational risk capital calculations," PSE-Ecole d'économie de Paris (Postprint) halshs-00443846, HAL.
    4. Dominique Guegan & Bertrand Hassani, 2009. "A new algorithm for the loss distribution function with applications to Operational Risk Management," Post-Print halshs-00384398, HAL.
    5. Dominique Guegan & Bertrand Hassani, 2009. "A new algorithm for the loss distribution function with applications to Operational Risk Management," Documents de travail du Centre d'Economie de la Sorbonne 09023, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Nov 2009.
    6. Hu, Xiang & Duan, Baige & Zhang, Lianzeng, 2017. "De Vylder approximation to the optimal retention for a combination of quota-share and excess of loss reinsurance with partial information," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 48-55.
    7. Sangüesa, C., 2008. "Error bounds in approximations of random sums using gamma-type operators," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 484-491, April.
    8. Richard L. Warr & Cason J. Wight, 2020. "Error Bounds for Cumulative Distribution Functions of Convolutions via the Discrete Fourier Transform," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 881-904, September.
    9. Yang Miao & Kristina P. Sendova, 2024. "Advantages of Accounting for Stochasticity in the Premium Process," Risks, MDPI, vol. 12(10), pages 1-25, October.
    10. Thomas Siller, 2013. "Measuring marginal risk contributions in credit portfolios," Quantitative Finance, Taylor & Francis Journals, vol. 13(12), pages 1915-1923, December.
    11. Paul Embrechts & Marco Frei, 2009. "Panjer recursion versus FFT for compound distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(3), pages 497-508, July.
    12. Pavel V. Shevchenko, 2010. "Calculation of aggregate loss distributions," Papers 1008.1108, arXiv.org.
    13. Valeriy A. Naumov & Yuliya V. Gaidamaka & Konstantin E. Samouylov, 2020. "Computing the Stationary Distribution of Queueing Systems with Random Resource Requirements via Fast Fourier Transform," Mathematics, MDPI, vol. 8(5), pages 1-9, May.
    14. Ruckdeschel, Peter & Kohl, Matthias, 2014. "General Purpose Convolution Algorithm in S4 Classes by Means of FFT," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 59(i04).
    15. Dominique Guegan & Bertrand Hassani, 2009. "A modified Panjer algorithm for operational risk capital calculations," Post-Print halshs-00443846, HAL.
    16. Vernic, Raluca, 2018. "On the evaluation of some multivariate compound distributions with Sarmanov’s counting distribution," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 184-193.
    17. Raluca Vernic, 2018. "On the Evaluation of the Distribution of a General Multivariate Collective Model: Recursions versus Fast Fourier Transform," Risks, MDPI, vol. 6(3), pages 1-14, August.
    18. Li Qin & Susan M. Pitts, 2012. "Nonparametric Estimation of the Finite-Time Survival Probability with Zero Initial Capital in the Classical Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 919-936, December.

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