Paper: arXiv 2603.06238

Authors: Jean-Loup Dupret, Edouard Motte

Abstract

In life insurance, life tables are used to estimate the survival distribution of individuals from a given population. However, these tables only provide survival probabilities at integer ages but no information about the distribution of deaths between two consecutive integer values. This incompleteness is particularly relevant for modern insurance products such as variable annuities, whose payoffs depend jointly on lifetime uncertainty and financial market performance. The valuation of such contracts must therefore be carried out in a joint actuarial-financial framework, as their values depend not only on the full information about mortality rates but also on the interaction between mortality risk, asset dynamics, and embedded guarantees. One frequent solution to this incompleteness is to postulate fractional age assumptions or mortality rate models, but it turns out that the results of the computations strongly depend on these restrictive assumptions. We hence derive upper and lower bounds of hybrid functionals of the lifetime with respect to mortality rates, which are compatible with the observed life table at integer ages and the given financial market. We derive two sets of results under distinct assumptions. In the first, we assume that each mortality trajectory is almost surely consistent with all the given one-year survival probabilities from the table. In the second, we consider a relaxed formulation that allows for deviations of the mortality rates while still being consistent in expectation with the given one-year reference survival probabilities. These distinct yet complementary approaches provide a new robust joint actuarial-financial framework for managing mortality risk in life insurance. They characterize the worst- and best-case contract values over all mortality processes that remain compatible with the observed life-table information and the financial market.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 4.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a sophisticated theoretical framework utilizing stochastic optimal control to derive bounds on hybrid actuarial-financial contract values under life table constraints. While mathematically rigorous and novel in its model-free mortality approach within a market-consistent setting, the excerpt focuses primarily on theoretical formulation with limited empirical backtesting provided in the intro.

Research Flowchart

  flowchart TD
    A[Research Goal: Derive robust bounds for hybrid actuarial-financial contract values without restrictive fractional age assumptions] --> B[Inputs: Integer-age Life Tables & Financial Market Asset Dynamics]
    
    B --> C[Framework 1: Strictly Consistent Trajectories<br/>A.S. consistency with 1-year survival probabilities]
    B --> D[Framework 2: Relaxed Consistency<br/>Consistency in expectation with reference probabilities]
    
    C --> E[Optimization: Compute Best- & Worst-Case Bounds over compatible mortality processes]
    D --> E
    
    E --> F[Outcomes: Model-free upper/lower bounds for Variable Annuities & robust mortality risk management]

Cited References (60)

  1. The statistical analysis of failure time data (2002)
  2. Actuarial Mathematics for Life Contingent Risks (2020)
  3. Option pricing: A simplified approach (1979)
  4. Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts (2004)
  5. Robust hedging of the lookback option (1998)
  6. Optimal stopping time problem in a general framework (2012)
  7. Model-independent bounds for option prices—a mass transport approach (2013)
  8. A stochastic control approach to no-arbitrage bounds given marginals, with an application to lookback options (2014) — link
and 52 more
  1. Affine processes for dynamic mortality and actuarial valuations (2005)
  2. Pricing death: Frameworks for the valuation and securitization of mortality risk (2006)
  3. American options and stochastic interest rates (2022)
  4. Stochastic Control of jump diffusions (2019)
  5. Valuation of guaranteed minimum accumulation benefits (GMABs) with physics-inspired neural networks (2024)
  6. Changes in Pure Premium Policy-Values consequent upon variations in the Rate of Interest or the Rate of Mortality, or upon the introduction of the Rate of Discontinuance (1905)
  7. On the application of Thiele’s differential equation in life insurance (1993)
  8. On the sensitivity of premiums and reserves to changes in valuation elements (2003)
  9. Lidstone in the continuous case (1985)
  10. Valuing American options by simulation: A simple least-squares approach (2001)
  11. Hedging of signature payoffs with temporary and permanent market impact (2025)
  12. Fredholm Approach to Nonlinear Propagator Models — → 2503.04323
  13. The uncertain mortality intensity framework: Pricing and hedging unit-linked life insurance contracts (2011)
  14. Robust assessment of life insurance products (2024)
  15. Uncertain volatility models with stochastic bounds (2018)
  16. Optimal stochastic control, stochastic target problems, and backward SDE (2012)
  17. Recursive valuation of defaultable securities and the timing of resolution of uncertainty (1996)
  18. Efficient hedging of life insurance portfolio for loss-averse insurers (2025)
  19. On life table applications of ordering among risks (1990)
  20. Statistical independence and fractional age assumptions (1997)
  21. A family of fractional age assumptions (2000)
  22. Comparison between future lifetime distribution and its approximations (2002)
  23. Properties of the power family of fractional age approximations (2003)
  24. Comparison and bounds for functionals of future lifetimes consistent with life tables (2012)
  25. Biometric worst-case scenarios for multi-state life insurance policies (2010)
  26. First-order mortality rates and safe-side actuarial calculations in life insurance (2010)
  27. Worst-case actuarial calculations consistent with single-and multiple-decrement life tables (2013)
  28. On the Nature of the Function Expressive of the Law of Human Mortality, and on a New Mode of Determining the Value of Life Contingencies (1825) — link
  29. On the Law of Mortality and the Construction of Annuity Tables (1860) — link
  30. The Age Pattern of Mortality (1980) — link
  31. Modeling and Forecasting U.S. Mortality (1992) — link
  32. A Two-Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration (2006) — link
  33. A Cohort-Based Extension to the Lee–Carter Model for Mortality Reduction Factors (2006) — link
  34. Coherent Mortality Forecasts for a Group of Populations: An Extension of the Lee–Carter Model (2005) — link
  35. Thirty years on: A review of the Lee–Carter method for forecasting mortality (2023)
  36. On the Approximation of Certain Life Insurance Functions (1961) — link
  37. Actuarial Mathematics (1997)
  38. Deep learning for high-dimensional continuous-time stochastic optimal control without explicit solution (2026)
  39. Deep Learning for Continuous-time Stochastic Control with Jumps — → 2505.15602
  40. Mortality modelling with L 'e vy processes (2008)
  41. Lee–Carter mortality forecasting with age-specific enhancement (2003)
  42. Point Processes (1980) — link
  43. A quantitative comparison of stochastic mortality models using data from E ngland and W ales and the U nited S tates (2009)
  44. On stochastic mortality modeling (2009)
  45. Applying Lee-Carter under conditions of variable mortality decline (2002)
  46. Smoothing and forecasting mortality rates with P -splines (2006)
  47. Risk-minimizing hedging strategies for unit-linked life insurance contracts (1998)
  48. Risk-minimizing hedging strategies for insurance payment processes (2001)
  49. Unit-linked life insurance policies: Optimal hedging in partially observable market models (2017)
  50. Option hedging for semimartingales (1991)
  51. On the minimal martingale measure and the M "o llmer- Schweizer decomposition (1995)
  52. Managing the volatility risk of portfolios of derivative securities: The L agrangian uncertain volatility model (1996)

2 of 60 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.