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

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  • Stefan Gerhold
  • Uwe Schmock
  • Richard Warnung

Abstract

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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

    as
    1. H. Panjer, Harry & Shaun Wang,, 1993. "On the Stability of Recursive Formulas," ASTIN Bulletin, Cambridge University Press, vol. 23(2), 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, Cambridge University Press, vol. 12(1), pages 27-39, June.
    4. Wang, Shaun & Sobrero, Monica, 1994. "Further Results on Hesselager's Recursive Procedure for Calculation of some Compound Distributions," ASTIN Bulletin, Cambridge University Press, vol. 24(2), pages 161-166, November.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Jonas Hirz & Uwe Schmock & Pavel V. Shevchenko, 2017. "Actuarial Applications and Estimation of Extended CreditRisk+," Risks, MDPI, vol. 5(2), pages 1-29, March.
    2. Ramírez-Cobo, Pepa & Carrizosa, Emilio & Lillo, Rosa E., 2021. "Analysis of an aggregate loss model in a Markov renewal regime," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    3. Dirk Tasche, 2015. "The Two Defaults Scenario for Stressing Credit Portfolio Loss Distributions," JRFM, MDPI, vol. 9(1), pages 1-18, December.
    4. Jonas Hirz & Uwe Schmock & Pavel V. Shevchenko, 2015. "Actuarial Applications and Estimation of Extended~CreditRisk$^+$," Papers 1505.04757, arXiv.org, revised Apr 2017.

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    More about this item

    Keywords

    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;
    All these keywords.

    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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