Convergence of Disturbed Martingales and a Stochastic Model for Annuity Funds

Abstract

Our aim is a stochastic model for the average income of a given annuity fund. Therefore we consider a special kind of stochastic process satisfying a condition of the form: In equation (0.1) denotes the income of the annuity fund at time n+1(future) and is the information about the money market up to time n(present). We wish to find conditions under which such a stochastic process is P-almost surely convergent and to determine whether or not there is a limiting income from our annuity fund. The question of L 1-convergence is also considered