Tails of random sums of a heavy-tailed number of light-tailed terms
By Christian-Yann Robert, Johan Segers. 2007
71 citations recorded by the source corpus.
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.
Subfields: Artificial Intelligence, Management Science and Operations Research, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/fd726b58447b5b8b34f31196d1afdf46fe0fdf38
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In Artificial Intelligence
In Management Science and Operations Research
In Mathematical Physics
Citations in the corpus
- Asymptotics for the ruin probabilities of a two-dimensional renewal risk model with heavy-tailed claims (2011, background): “[5], Tang [6, 7], Wang and Wang [8], Robert and Segers [9], Aleškevičienė et al.”
- Sums of Pairwise Quasi-Asymptotically Independent Random Variables with Consistent Variation (2009, unknown): “80 Chen and Yuen Robert and Segers[25].”
- The Strong Law of Large Numbers for Extended Negatively Dependent Random Variables (2010, unknown): “Motivated by Corollary 3.1 of Ko and Tang (2008), in the following lemma we show a sufficient condition for the random variables Xk, k = 1, . . . , n, to be LEND or UEND.”