Confidence Bounds for Discounted Loss Reserves

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 in Doray, 1996. 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. 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