Hits:

Indexed by:期刊论文

Date of Publication:2013-03-01

Journal:METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY

Included Journals:SCIE

Volume:15

Issue:1

Page Number:165-186

ISSN No.:1387-5841

Key Words:Compound renewal risk model; Ruin probability; Consistent variation; Asymptotically quadrant sub-independent; Markov environment process

Abstract:In this paper, we consider the random sums of one type of asymptotically quadrant sub-independent and identically distributed random variables {X, X (i) , i = 1, 2, a <-aEuro parts per thousand} with consistently varying tails. We obtain the asymptotic behavior of the tail under different cases of the interrelationships between the tails of X and eta, where eta is an integer-valued random variable independent of {X, X (i) , i = 1, 2, a <-aEuro parts per thousand}. We find out that the asymptotic behavior of is insensitive to the dependence assumed in the present paper. We state some applications of the asymptotic results to ruin probabilities in the compound renewal risk model under dependent risks. We also state some applications to a compound collective risk model under the Markov environment.