Precise local large deviations for heavy-tailed random sums with applications to risk models

Abstract

In this paper, we investigate the precise local large deviation probabilities for random sums of independent real-valued random variables with a common heavy-tailed distribution F, where is an -regularly varying function for some fixed constant (finite or infinite). We also obtain some results on precise local large deviation probabilities for the claim surplus process of generalized risk models in which the premium income until time t is simply assumed to be a nondecreasing and nonnegative stochastic process. In particular, the results we obtained are also valid for the global case, i.e. case .