# Rapidly bounding the exceedance probabilities of high aggregate losses 

Department of Engineering University of Bristol 

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 

Isabella Gollini ∗ 

November 5, 2018 

## Abstract 

Jonathan Rougier 

Department of Mathematics University of Bristol 

