Asymptotic Behavior of Ruin Probability in Insurance Risk Model with Large Claims

For the renewal risk model with subexponential claim sizes, we established for the finite time ruin probability a lower asymptotic estimate as initial surplus increases, subject to the demand that it should hold uniformly over all time horizons in an infinite interval. In the case of Poisson model, we also obtained the upper asymptotic formula so that an equivalent formula was derived. These extended a recent work partly on the topic from the case of Pareto-type claim sizes to the case of subexponential claim sizes and, simplified the proof of lower bound in Leipus and Siaulys ([9]).