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Computation of Compound Distributions II: Discretization Errors and Richardson Extrapolation

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  • Grübel, Rudolf
  • Hermesmeier, Renate

Abstract

The standard methods for the calculation of total claim size distributions and ruin probabilities, Panjer recursion and algorithms based on transforms, both apply to lattice-type distributions only and therefore require an initial discretization step if continuous distribution functions are of interest. We discuss the associated discretization error and show that it can often be reduced substantially by an extrapolation technique.

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  • Grübel, Rudolf & Hermesmeier, Renate, 2000. "Computation of Compound Distributions II: Discretization Errors and Richardson Extrapolation," ASTIN Bulletin, Cambridge University Press, vol. 30(2), pages 309-331, November.
    • Handle: RePEc:cup:astinb:v:30:y:2000:i:02:p:309-331_01
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    Cited by:

    1. 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.
    2. Sanguesa, C., 2006. "Approximations of ruin probabilities in mixed Poisson models with lattice claim amounts," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 69-80, August.
    3. 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.
    4. 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.
    5. 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.
    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. 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.
    8. 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.

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