Asymptotic ruin probabilities in a discrete-time risk model with heavy-tailed random sums

In this paper, we consider a discrete time insurance risk model with some large classes of heavy-tailed claim distributions. we show that the probabilities of the maxima of the partial sums asymptotically equal to the sum of the tail probabilities of the individual random variables. We will study partially the asymptotic property extending the result to of ruin probabilities for some large classes of heavy-tailed distributions.Finally some numerical illustrations are given.

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