A Recursive Scheme for Perpetuities with Random Positive Interest Rates. II: The Impenetrable Wall

In some former contributions, the authors investigated actuarial quantities with stochastic interest rates. In a first model, the randomness is modelled by means of an ordinary Wiener process, and as a consequence negative interest rates are possible. A second model provides a tool to avoid these negative interest rates, which can be necessary in particular situations. This paper wants to present an alternative solution to the problem of negative interest rates. This new model will be implemented to the case of an annuity certain and of a perpetuity.