Tails of random sums of a heavy-tailed number of light-tailed terms

The tail of the distribution of a sum of a random number of independent and identically distributed nonnegative random variables depends on the tails of the number of terms and of the terms themselves. This situation is of interest in the collective risk model, where the total claim size in a portfolio is the sum of a random number of claims. If the tail of the claim number is heavier than the tail of the claim sizes, then under certain conditions the tail of the total claim size does not change asymptotically if the individual claim sizes are replaced by their expectations. The conditions allow the claim number distribution to be of consistent variation or to be in the domain of attraction of a Gumbel distribution with a mean excess function that grows to infinity sufficiently fast. Moreover, the claim number is not necessarily required to be independent of the claim sizes.

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Document type	Document de travail (Working Paper)
Access type	Accès libre
Publication date	2007
Language	Anglais
Number of pages	18 pages
Collection	STAT Discussion Paper - 0704
Affiliation	UCL - EUEN/STAT - Institut de statistique
Keywords	Compound distribution ; Collective risk model ; Consistent variation ; Heavy-tailed distributions ; Light-tailed distributions ; Large deviations ; Random sum
Links	http://sites.uclouvain.be/IAP-Stat-Phase-V-VI/ISBApub/ISBAdp.html#2007 http://hdl.handle.net/2078.1/114912[Handle]

See also
	[boreal:36974]	Tails of random sums of a heavy-tailed number of light-tailed terms