Lower Asymptotics for the Finite Time Ruin Probability in the Renewal Model with Subexponential Claims

摘要

For the renewal risk model with subexponential claim sizes, we establish 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. This extends a recent work partly on the topic from the case of Pareto-type claim sizes to the case of subexponential claim sizes and, simplifies the proof of lower bound in Leipus and Siaulys (2006).