Finance and Stochastics

, 14:81 | Cite as

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

  • Stefan Gerhold
  • Uwe Schmock
  • Richard Warnung


Portfolio credit risk models as well as models for operational risk can often be treated analogously to the collective risk model coming from insurance. Applying the classical Panjer recursion in the collective risk model can lead to numerical instabilities, for instance if the claim number distribution is extended negative binomial or extended logarithmic. We present a generalization of Panjer’s recursion that leads to numerically stable algorithms. The algorithm can be applied to the collective risk model, where the claim number follows, for example, a Poisson distribution mixed over a generalized tempered stable distribution with exponent in (0,1). De Pril’s recursion can be generalized in the same vein. We also present an analogue of our method for the collective model with a severity distribution having mixed support.


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 

Mathematics Subject Classification (2000)

91B30 65Q05 62P05 

JEL Classification

C63 C16 


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Institute for Mathematical Methods in EconomicsVienna University of TechnologyViennaAustria
  2. 2.RisikomanagementRaiffeisen Capital ManagementViennaAustria

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