Abstract: A dual random model of a portfolio of variable amount whole life annuity is set with the mth moment of the present value of benefits, and the respective expressions of the moments under the assumption that the force of interest accumulation function is Wiener process or Ornstein-Uhlenbeck process. Furthermore, the limiting distribution of average cost of this portfolio is discussed with the expression of the limiting distribution under the assumption that the force of interest accumulation is an independent increment process.

Key words: Whole life annuity policy, Force of interest, Present value of benefit, Moment, Limiting distribution, Wiener process, Ornstein-Uhlenbeck process, Independent increment process

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