Momnts and limiting distribution of a portfolio of whole life annuity pollcies

A dual random model of a portfolio of variable amount whole life anunity is set with the mth moment of the present value of benefits.and the respective expressions of the monments under the assumption that the force of interest accumulation fuction is Wiener process of Omstein-Uhlenbeck process,Furthermore,the limiting dstribution of average cost of this protfolio is discussed with the expression of the limiting distribution under the assumption that the force of interest accumulation is an independent increment process.