Annuities Under Changes in Life Tables and Changes in the Interest II

Abstract

In a previous paper [Z] we achieved some estimates for the changes in life annuities due to changes in the force of mortality and the force of interest, and we derived estimates for the change in annuities and other classical vales for life assurance under a change in the force of interest and the force of mortality. Dynamical life tables (DLT) use force of mortality that varies with time. Life insurance plans and pension schemes are recently considering DLT and variable rate of interest. Evaluation of annuities subject to DLT is quite complex. We suggest approximations based on the estimates that we achieved in (Z). Annuities serve as parameters in evaluating the classical values of assurances, premiums and reserves. One can express changes in premiums and reserves in terms of the estimates under the changes in life expectancy and the force of interest. One can use similar ideas to estimate the risk arising from the difference of the volatility of the premiums and that of the liabilities. This may lead to an immunization policy of investing premiums considering the liabilities. We expand the results of (Z) to higher derivatives. This will enable us to achieve better estimates and to evaluate the size of the error of the estimated values.