Dupret and Motte derive variable annuity value bounds from life tables

In context: this report covers a source published on 21 Oct 2026.

Life tables give the probability of surviving each whole year of age, but they say nothing about when deaths fall within a year. Actuaries usually fill that gap with a fractional-age rule or a mortality model, which adds model risk. In a preprint on arXiv, which is not peer reviewed, Jean-Loup Dupret and Edouard Motte ask how far the value of contracts that depend on both lifetime and markets, such as variable annuities, can move across all mortality patterns consistent with the table. The current third version was posted on 21 October 2026; the first appeared in March.

The authors calculate best-case and worst-case values for three guarantees: minimum accumulation (GMAB), income (GMIB) and death (GMDB) benefits. In a strict version, each mortality path must match every one-year survival probability in the table. In a relaxed version, the table must hold only on average, around a baseline mortality rate. The market side has a stock and a stochastic short rate that can be correlated. The worked examples use a Belgian female life table, policyholders aged 40, 60 and 80, and illustrative market parameters.

In the paper's strict model, the upper and lower GMAB bounds coincide, so under those assumptions the value of that guarantee does not depend on how deaths fall within each year. The authors describe the GMIB bounds as 'relatively narrow', and the choice among three standard fractional-age rules had 'virtually no impact' on price; gaps grow at older ages and longer maturities. Matching only on average gives wider bounds that are lopsided: for the survival benefits the lower bound falls far below the baseline, while for the death benefit the upper bound sits far above it. Adding constraints at intermediate dates narrowed the GMIB and GMDB bounds.

The paper does not price a real product or use company data, and it reports results only as charts. For the relaxed case the authors fixed interest rates and simplified the model to keep the calculation manageable; they expect similar behaviour in the full model but do not show it. They also say wide strict bounds mainly signal information missing from the table, not plausible scenarios. The methods are optimisation and Monte Carlo simulation; deep learning is suggested only for future extensions.