  In this paper we consider a stochastic model of perpetuity-type. In contrast
to the classical affine perpetuity model of Kesten [12] and Goldie [8] all
discount factors in the model are mutually independent. We prove that the tails
of the distribution of this model are regularly varying both in the univariate
and multivariate cases. Due to the additional randomness in the model the tails
are not pure power laws as in the Kesten-Goldie setting but involve a
logarithmic term.
