Annuities Under Changes in Life Tables and Changes in the Interest III or, Premium Increases When Interest Decreases

Abstract

In a previous paper [Z1] we suggested to unify the study of changes in life annuities due to changes in the force of mortality and the force of interest, and we proposed estimates for the change in annuities , liabilities of life assurance, premiums and reserves 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 suggested in [Z2] some approximations based on the estimates that we achieved in [Z1]. Annuities may serve to evaluate the values of assurances, premiums, provisions and reserves. We will investigate the changes in premiums to show that premiums increase when interest decreases. Since the marginal change in the premium equals the difference between the volatility of the annuities and the volatility of the liabilities one may derive that the volatility of the liabilities is greater than the volatility of the annuities. This observation may serve to an immunization policy that arises when considering the cash flow of income and liabilities.