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Different interpolations of yearly life tables produce nearly identical or substantially different IASU decompositions of life insurance surplus.

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2026-06-28 03:25 UTC pith:6A466NMA

load-bearing objection Constant interpolation of yearly life tables produces clearly different IASU surplus decompositions than linear or Lee-Carter methods.

arxiv 2606.04715 v1 pith:6A466NMA submitted 2026-06-03 q-fin.ST

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

Mintod\^e Nicod\`eme Atchad\'e , Marcus C. Christiansen , Friedrich Hubalek , Gero Junike This is my paper
classification q-fin.ST
keywords life insurance surplusIASU decompositionlife table interpolationLee-Carter modelmortality risk attributionShapley valuecontinuous-time decomposition
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper applies the IASU decomposition, a continuous-time Shapley-value method, to split life insurance surplus changes into mortality and financial components. It tests how three ways of filling in values between annual life-table updates affect the resulting attributions. Lee-Carter and linear interpolation produce almost the same splits, while constant approximations produce markedly different ones. A reader would care because companies and regulators rely on such decompositions for reporting and risk management, and the choice of interpolation is not neutral.

Core claim

When mortality inputs come from interpolating discrete annual life tables rather than continuous observation, the IASU decomposition still attributes surplus changes, but the numerical results depend strongly on the interpolation rule: Lee-Carter and linear rules agree closely while constant rules diverge substantially.

What carries the argument

The IASU decomposition, a continuous-time version of the Shapley value that attributes surplus changes between mortality and financial risk factors.

Load-bearing premise

The IASU decomposition remains a valid attribution tool when mortality inputs are obtained by interpolating discrete annual life tables rather than observed continuously.

What would settle it

Compute the IASU decomposition on a portfolio whose true continuous mortality path is known, then repeat the calculation using each interpolation rule on the same annual snapshots; large, systematic differences in the attributed mortality share across rules would falsify the claim that the method is robust to interpolation choice.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Reporting standards must specify an interpolation method to ensure comparable surplus decompositions across insurers.
  • Constant approximations cannot be treated as interchangeable with Lee-Carter or linear methods without changing the attributed sources of surplus.
  • Lee-Carter and linear interpolation can be used interchangeably for most practical attribution purposes without material change in results.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Linear interpolation may serve as a simpler, equally reliable substitute for Lee-Carter in routine surplus reporting.
  • The sensitivity to interpolation suggests that any regulatory framework for life-insurance surplus should include explicit rules for handling intra-year mortality updates.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

0 major / 2 minor

Summary. The manuscript proposes the IASU decomposition (a continuous-time Shapley-value attribution) for life-insurance surplus arising from mortality and financial changes. Because life tables are observed only annually, it applies three interpolation schemes (Lee-Carter, linear, and constant) to produce continuous mortality paths and then compares the resulting IASU decompositions, reporting that Lee-Carter and linear interpolation produce nearly identical attributions while constant approximation yields substantially different ones; it concludes that reporting standards should specify an interpolation convention.

Significance. If the empirical comparison is robust, the work shows that the choice of interpolation method can materially affect the attribution of surplus between mortality and financial drivers, with direct implications for internal reporting and regulatory disclosure. The explicit use of an axiomatically justified continuous-time operator is a methodological strength.

minor comments (2)
  1. [Abstract] Abstract: the comparative claims are stated without any numerical magnitudes, data description, sample sizes, or error measures, so the reader cannot gauge whether the reported differences are economically large or statistically stable.
  2. The manuscript would benefit from a short table or figure that quantifies the decomposition differences (e.g., percentage-point deviations in the mortality versus financial components) across the three interpolation methods for at least one representative policy.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of the manuscript, the recognition of the methodological contribution of the IASU decomposition, and the recommendation for minor revision. No specific major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper applies a fixed, axiomatically justified IASU operator (continuous-time Shapley value) consistently to mortality paths generated by each interpolation method. The central result is an empirical comparison showing that Lee-Carter and linear interpolation produce nearly identical decompositions while constant approximation differs; this comparison does not reduce to any fitted parameter, self-definition, or self-citation chain. No load-bearing step equates a prediction to its input by construction, and the IASU construction is treated as an external operator rather than derived within the paper. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review yields minimal ledger entries; the sole domain assumption is the axiomatic status of IASU.

axioms (1)
  • domain assumption IASU decomposition is an axiomatically justified continuous-time version of the Shapley value.
    Invoked in the abstract as the chosen decomposition method.

pith-pipeline@v0.9.1-grok · 5660 in / 1062 out tokens · 36999 ms · 2026-06-28T03:25:18.376713+00:00 · methodology

0 comments
read the original 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.

Figures

Figures reproduced from arXiv: 2606.04715 by Friedrich Hubalek, Gero Junike, Marcus C. Christiansen, Mintod\^e Nicod\`eme Atchad\'e.

Figure 1
Figure 1. Figure 1: Survival probability St and contribution of mortality risk estimated from life tables from 2005 - 2020 using different interpolation methods for fractional years. Panel A: Survival probability St. Panel B: contribution of mortality risk for N = 100 000 using yearly SU or ASU with daily data. The contribution is calculated every year and the reporting date is set to the middle of the year. Declarations Conf… view at source ↗

discussion (0)

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Reference graph

Works this paper leans on

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