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Panjer recursion versus FFT for compound distributions

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  • Paul Embrechts
  • Marco Frei

Abstract

Numerical evaluation of compound distributions is an important task in insurance mathematics and quantitative risk management. In practice, both recursive methods as well as transform based techniques are widely used. We give a survey of these tools, point out the respective merits and provide some numerical examples. Copyright Springer-Verlag 2009

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:69:y:2009:i:3:p:497-508
    DOI: 10.1007/s00186-008-0249-2
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    References listed on IDEAS

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    1. Gerber, Hans U., 1982. "On the numerical evaluation of the distribution of aggregate claims and its stop-loss premiums," Insurance: Mathematics and Economics, Elsevier, vol. 1(1), pages 13-18, January.
    2. H. Panjer, Harry & Shaun Wang,, 1993. "On the Stability of Recursive Formulas," ASTIN Bulletin, Cambridge University Press, vol. 23(2), pages 227-258, November.
    3. Marco Moscadelli, 2004. "The modelling of operational risk: experience with the analysis of the data collected by the Basel Committee," Temi di discussione (Economic working papers) 517, Bank of Italy, Economic Research and International Relations Area.
    4. 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.
    5. 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.
    6. Sundt, Bjørn, 1999. "On Multivariate Panjer Recursions," ASTIN Bulletin, Cambridge University Press, vol. 29(1), pages 29-45, May.
    7. Sundt, Bjørn & Jewell, William S., 1981. "Further Results on Recursive Evaluation of Compound Distributions," ASTIN Bulletin, Cambridge University Press, vol. 12(1), pages 27-39, June.
    8. Panjer, Harry H. & Willmot, Gordon E., 1986. "Computational aspects of recursive evaluation of compound distributions," Insurance: Mathematics and Economics, Elsevier, vol. 5(1), pages 113-116, January.
    9. Vernic, Raluca, 1999. "Recursive Evaluation of Some Bivariate Compound Distributions," ASTIN Bulletin, Cambridge University Press, vol. 29(2), pages 315-325, November.
    10. Bladt, Mogens, 2005. "A Review on Phase-type Distributions and their Use in Risk Theory," ASTIN Bulletin, Cambridge University Press, vol. 35(1), pages 145-161, May.
    11. Panjer, Harry H., 1981. "Recursive Evaluation of a Family of Compound Distributions," ASTIN Bulletin, Cambridge University Press, vol. 12(1), pages 22-26, June.
    12. Hesselager, Ole, 1996. "Recursions for certain bivariate counting distributions and their compound distributions," ASTIN Bulletin, Cambridge University Press, vol. 26(1), pages 35-52, May.
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    Cited by:

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    3. J. D. Opdyke, 2014. "Estimating Operational Risk Capital with Greater Accuracy, Precision, and Robustness," Papers 1406.0389, arXiv.org, revised Nov 2014.
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    7. 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.
    8. J. D. Opdyke, 2016. "Fast, Accurate, Straightforward Extreme Quantiles of Compound Loss Distributions," Papers 1610.03718, arXiv.org, revised Jul 2017.
    9. Denuit, Michel & Trufin, Julien, 2016. "Collective Loss Reserving with Two Types of Claims in Motor Third Party Liability Insurance," LIDAM Discussion Papers ISBA 2016029, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Fallou Niakh, 2023. "A fixed point approach for computing actuarially fair Pareto optimal risk-sharing rules," Papers 2303.05421, arXiv.org, revised Jul 2023.
    11. Muneya Matsui, 2017. "Prediction of Components in Random Sums," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 573-587, June.
    12. 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.
    13. Fomichov, Vladimir & González Cázares, Jorge & Ivanovs, Jevgenijs, 2021. "Implementable coupling of Lévy process and Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 407-431.
    14. Zhou, Xiaoping & Durfee, Antonina V. & Fabozzi, Frank J., 2016. "On stability of operational risk estimates by LDA: From causes to approaches," Journal of Banking & Finance, Elsevier, vol. 68(C), pages 266-278.
    15. Dirk Tasche, 2015. "The Two Defaults Scenario for Stressing Credit Portfolio Loss Distributions," JRFM, MDPI, vol. 9(1), pages 1-18, December.
    16. Marios N. Kyriacou, 2015. "Credit Risk Measurement in Financial Institutions: Going Beyond Regulatory Compliance," Cyprus Economic Policy Review, University of Cyprus, Economics Research Centre, vol. 9(1), pages 31-72, June.
    17. H'el`ene Cossette & Benjamin C^ot'e & Alexandre Dubeau & Etienne Marceau, 2024. "Risk models from tree-structured Markov random fields following multivariate Poisson distributions," Papers 2412.00607, arXiv.org.
    18. Pavel V. Shevchenko, 2010. "Calculation of aggregate loss distributions," Papers 1008.1108, arXiv.org.
    19. Pavel V. Shevchenko, 2009. "Implementing Loss Distribution Approach for Operational Risk," Papers 0904.1805, arXiv.org, revised Jul 2009.
    20. Denuit, Michel & Trufin, Julien, 2016. "Beyond the Tweedie Reserving Model: The Collective Approach to Loss Development," LIDAM Discussion Papers ISBA 2016030, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    21. Gareth W. Peters & Pavel V. Shevchenko & Mario V. Wuthrich, 2009. "Dynamic operational risk: modeling dependence and combining different sources of information," Papers 0904.4074, arXiv.org, revised Jul 2009.

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