Entropy and duration in life annuity valuation: a closed-form decomposition

This paper develops a financially adjusted life-table framework for analysing the timing structure of annuity payments. Within this framework, we introduce a financially adjusted entropy measure that captures the dispersion of discounted survival mass underlying life-contingent cash flows. We show that this quantity admits a closed-form additive decomposition into two actuarial indicators already known in the literature: Haberman's annuity entropy and Salinelli's duration. The resulting identity establishes a direct analytical link between demographic and financial sensitivities in annuity valuation. Numerical illustrations based on Human Mortality Database data and stochastic mortality projections confirm the validity of the decomposition and demonstrate how the proposed indicators capture differences in the timing structure of annuity liabilities even when portfolios have identical expected present values.