Decomposing changes in life annuities

This paper proposes a novel approach for assessing changes in the expected present value of life annuities by adapting decomposition techniques traditionally applied in demographic research. Building upon Vaupel and Canudas–Romo’s method, a closed-form relationship is derived within the continuous framework to express changes in the expected present value of life annuities. By employing commutation functions, the concept of financially adjusted life-table entropy is introduced to capture the inter- play between mortality and interest rate changes, offering a new and comprehensive measure for evaluating annuity price sensitivity. The approach is illustrated through a numerical application using life tables from Italy and the United Kingdom.