Estimation of the Present Values of Life Annuities for the Different Actuarial Models

The paper deals with the problem of estimating the actuarial present value of the continuous whole life and n-year term life annuities. We synthesize nonparametric estimators of these statuses of life annuity. The main parts of their asymptotic mean square errors for these estimators and their limit distributions are found. By individuals' death moments, both parametric and nonparametric estimates are constructed for the models of the whole and n-year term life insurance. The asymptotic normality and mean square convergence of the proposed estimators are proved. The simulations show that the empirical mean square errors of life annuity estimates decrease when the sample size increases. Also, when the model distribution is changed, the nonparametric estimates are more adaptable in comparison with parametric estimates, oriented on the best results only for the given distributions.