Insurance considering a new stochastic model for the discount factor

Abstract

In many empirical situations (e.g.:Libor), the rate of interest will remain fixed at a certain level(random instantaneous rate &i) for a random period of time(ti) until a new random rate should be considered, &i+ 1, that will remain for ti+ 1, waiting time untill the next change in the rate of interest. Three models were developed using the approach cited aboye for random rate of interest and random waiting times between changes in the rate of interest. Using easy integral transforms (Laplace and Fourier) we will be able to ca1culate the moments of the probability function of the discount factor, V(t),and even its c.dJ. The approach will also be extended to the calculation of the expected value(net premium) and variance of a term insurance and we will get its c.d.f., something not very common in actuarialliterature due to its complexity, but very useful when the law of large numbers cannot be applied and consequently use normal approximations.