IBNR Reserve Under a Loglinear Location-Scale Regression Model

In this paper, we develop models for known claims, when the data are grouped into the usual triangle and the goal is to predict IBNR claims. We assume that the payment for a certain accident and development year is composed of a deterministic part and a multiplicative random error. We use a loglinear location-scale regression model for the amount of claims. The parameters are estimated by maximum likelihood methods, so that their asymptotic properties are well known. The regression model presents many advantages over the chain ladder method: it has fewer parameters, and does not underestimate the reserve. Moreover, it will be possible with a simulation to establish a reserve with a certain level of confidence (for example 80%). We advocate the use of regression models over the chain ladder method, since they take into account both the error involved in the estimation of the parameters and the statistical error inherent in the prediction of future claims, the fit of the model can be tested statistically and confidence intervals for the reserve can be derived. Keywords: chain ladder, maximum likelihood, consistency.