Abstract
In this paper, we establish the second order asymptotics of ruin probabilities of a renewal risk model under the condition that the equilibrium distribution of claim sizes belongs to a rather general heavy-tailed distribution subclass—the class of second order subexponential distributions with finite mean. What is more, this requirement is proved to be necessary. Furthermore, a rather general sufficient condition on the claim size distribution itself is presented. Moreover, an extension to the case of random walk is also included.
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