Some improvements on the Lundberg bound for the ruin probability

In this paper, improvements on the Lundberg bound for the ruin probability in the classical risk model are considered. First, a lower bound and an upper bound are derived in terms of an NWU and NBU distribution which generalize the Lundberg bound based on the exponential distribution. Second, some new techniques are developed based on the classical renewal theory. Extensions to more general cases are discussed. Application to the Weibull model is used for illustration.