In this paper we give some methods to set up confidence bounds for the discounted IBNR reserve. We start with a loglinear regression model and estimate the parameters by maximum likelihood such as given, for example, by Doray [Insur.: Math. Econ. 18 (1996) 43]. The knowledge of the distribution function of the discounted IBNR reserve (S) will help us to determine the initial reserve, for example, through the 95th percentile F-S(-1) (0.95). The results are based on convex order techniques, such that our approximations for the distribution function of S are larger or smaller, in convex order sense, than the true distribution function of S. (C) 2003 Elsevier B.V. All rights reserved.