A Statistical Approach to IBNR Reserves

This paper develops a three dimensional statistical approach to the estimation of the mean and the standard deviation of pure incurred but not reported (IBNR) reserves. This means that the time of occurrence, the reporting lag, and the claim severity are separately modeled. It is assumed that, beyond any fixed time $t$, the claim number development process is Poisson and that the severity of loss depends on the length of the reporting lag. Two key assumptions are made to simplify the estimation of model parameters: for a given reporting lag, (i) the conditional mean of the claim size is a linear function of the reporting lag, and (ii) the conditional coefficient of variation of the severity is constant.