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A generalization of Panjer’s recursion and numerically stable risk aggregation


  • Stefan Gerhold


  • Uwe Schmock


  • Richard Warnung



No abstract is available for this item.

Suggested Citation

  • Stefan Gerhold & Uwe Schmock & Richard Warnung, 2010. "A generalization of Panjer’s recursion and numerically stable risk aggregation," Finance and Stochastics, Springer, vol. 14(1), pages 81-128, January.
  • Handle: RePEc:spr:finsto:v:14:y:2010:i:1:p:81-128
    DOI: 10.1007/s00780-009-0104-1

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    References listed on IDEAS

    1. H. Panjer, Harry & Shaun Wang, 2, 1993. "On the Stability of Recursive Formulas," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 23(02), pages 227-258, November.
    2. Gordy, Michael B., 2002. "Saddlepoint approximation of CreditRisk+," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1335-1353, July.
    3. Sundt, Bjørn & Jewell, William S., 1981. "Further Results on Recursive Evaluation of Compound Distributions," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 12(01), pages 27-39, June.
    4. L. Randall Wray & Stephanie Bell, 2004. "Introduction," Chapters,in: Credit and State Theories of Money, chapter 1 Edward Elgar Publishing.
    5. Philippe Robert-Demontrond & R. Ringoot, 2004. "Introduction," Post-Print halshs-00081823, HAL.
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    Cited by:

    1. repec:gam:jjrfmx:v:9:y:2015:i:1:p:1:d:61528 is not listed on IDEAS
    2. repec:gam:jrisks:v:5:y:2017:i:2:p:23-:d:94636 is not listed on IDEAS
    3. Jonas Hirz & Uwe Schmock & Pavel V. Shevchenko, 2015. "Actuarial Applications and Estimation of Extended~CreditRisk$^+$," Papers 1505.04757,, revised Apr 2017.
    4. Dirk Tasche, 2015. "The Two Defaults Scenario for Stressing Credit Portfolio Loss Distributions," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 9(1), pages 1-18, December.

    More about this item


    Portfolio credit risk; CreditRisk + ; Operational risk; Collective risk model; Extended negative binomial distribution; Extended logarithmic distribution; Compound distribution; Extended Panjer recursion; Numerical stability; De Pril’s recursion; Poisson mixture distribution; Generalized tempered stable distribution; (Generalized) inverse Gaussian distribution; Reciprocal generalized inverse Gaussian distribution; Inverse gamma distribution; Severities with mixed support; 91B30; 65Q05; 62P05; C63; C16;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions


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