How the interpolation of life tables affects the decomposition of life insurance surplus

Mintod\^e Nicod\`eme Atchad\'e, Marcus C. Christiansen, Friedrich Hubalek and Gero Junike

Papers from arXiv.org

Abstract: The surplus of a life insurance policy depends on both systematic changes in mortality risk and financial changes. We propose to decompose the surplus by the axiomatically justified IASU decomposition, which is a continuous time version of the Shapley value. However, life tables are not updated continuously, but rather, only once per year. In this yearly update cycle of the life tables, we apply different interpolation methods to perform the IASU decomposition and analyze the effects of these methods on the surplus decomposition. Our results show that Lee-Carter and linear interpolation yield almost identical decompositions, whereas constant approximations results in substantially different decompositions. As a consequence, reporting standards and regulators should clarify how to interpolate mortality risks.

Date: 2026-06
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