Precise Large Deviations for Subexponential Distributions in a Multi Risk Model

The precise large deviations asymptotics for the sums of independent identical random variables when the distribution of the summand belongs to the class S ∗ of heavy tailed distributions is studied. Under mild conditions, we extend the previous results from the paper Denisov et al. (2010) to asymptotics that are valid uniformly over some time interval. Finally, we apply the main result on the multi-risk model introduced by Wang and Wang (2007)