IBNR reserves under stochastic interest rates

This paper intends to evaluate the present value of incurred but not reported (IBNR) reserves, when future interest rates are unknown. We first derive a result for the Laplace transform of the present value, when it is assumed that the interest rates are stochastic and can be modelled by means of a stochastic process which is similar to the model of Cox et al. (1985). Starting from this Laplace transform, it is shown how the probability distribution for the quantity under investigation can be found. The results are illustrated numerically.