Rapidly bounding the exceedance probabilities of high aggregate losses Isabella Gollini ∗ Department of Engineering University of Bristol Jonathan Rougier Department of Mathematics University of Bristol November 5, 2018 We consider the task of assessing the righthand tail of an insurer’s loss distribution for some specified period, such as a year. We present and analyse six different approaches: four upper bounds, and two approx- imations. 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 favour 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 favour the Gamma distribution as a flexible model for single event losses, for its tractable form in all of the methods we analyse, its generalisability, and because of the ease with which a cap on losses can be incorporated. KEYWORDS: Event loss table, Compound Poisson process, Moment bound, Monte Carlo simulation Abstract arXiv:1507.01853v1 [stat.AP] 7 Jul 2015 $^{∗}$Corresponding author. email: isabella.gollini@bristol.ac.uk 1