Journal of Operational Risk

Rapidly bounding the exceedance probabilities of high aggregate losses

Isabella Gollini and Jonathan Rougier

  • Moment bound offers the best blend of tightness and computational efficiency.
  • Moment bound can help to rapidly evaluate the worst case scenarios.
  • Encourage the use of the capped Gamma distribution over the Beta distribution.
  • The tailloss package for R has been implemented to carry out the analysis.


We consider the task of assessing the right-hand tail of an insurer's loss distribution for some specified period, such as a year. We present and analyze six different approaches: four upper bounds and two approximations. We examine these approaches under a variety of conditions, using a large event loss table for US hurricanes. For its combination of tightness and computational speed, we favor the moment bound. We also consider the appropriate size of Monte Carlo simulations and the imposition of a cap on single-event losses.We strongly favor the Gamma distribution as a flexible model for single-event losses, because of its tractable form in all of the methods we analyze, its generalizability and the ease with which a cap on losses can be incorporated into it.

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