IBNR Reserves Under Stochastic Interest Rates

This paper intends to evaluate the present value of IBNR reserve, when future interest rates are unknown. The authors 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. 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.

Keywords: IBNR reserves; Discount factor; Probability density; Laplace transform