[Paper Review] Etude du risque syst\\'ematique de mortalit\\'e

Frédéric Planchet, Laurent Faucillon+1 more|arXiv (Cornell University)|Jan 12, 2010

Insurance, Mortality, Demography, Risk Management3 citations

TL;DR

This paper proposes a stochastic mortality model based on the Lee-Carter framework to quantify systematic mortality risk in pension liabilities. By projecting random future mortality rates, it enables robust risk assessment and hedging strategies for retirement obligations, offering a practical tool for insurers and institutional investors.

ABSTRACT

The aim of this paper is to propose a realistic and operational model to quantify the systematic risk of mortality included in an engagement of retirement. The model presented is built on the basis of model of Lee-Carter. The stochastic prospective tables thus built make it possible to project the evolution of the random mortality rates in the future and to quantify the systematic risk of mortality.

Motivation & Objective

• To develop a realistic and operational model for measuring systematic mortality risk in long-term retirement obligations.
• To extend the Lee-Carter model with stochastic projections to capture uncertainty in future mortality trends.
• To provide actuaries and financial institutions with a quantifiable framework for pricing and hedging longevity risk.
• To assess the financial impact of unexpected improvements in mortality rates on pension fund solvency.
• To support risk management decisions through stochastic mortality tables that reflect systematic risk exposure.

Proposed method

• The Lee-Carter model is adapted to include stochastic components in the time-varying parameter to reflect random fluctuations in mortality trends.
• Monte Carlo simulations are used to generate multiple stochastic mortality trajectories over time.
• Stochastic prospective mortality tables are constructed to project future mortality rates under various random scenarios.
• Systematic risk is quantified by analyzing the variance and distribution of projected mortality rates across simulations.
• The model incorporates historical mortality data to calibrate parameters and ensure realism in projections.
• Risk measures such as Value-at-Risk and expected shortfall are applied to the simulated mortality outcomes to assess financial exposure.

Experimental results

Research questions

• RQ1 How can systematic mortality risk in pension liabilities be quantified using a stochastic mortality model?
• RQ2 To what extent do random fluctuations in mortality trends affect long-term pension fund solvency?
• RQ3 Can the Lee-Carter model be enhanced with stochasticity to better reflect real-world uncertainty in mortality projections?
• RQ4 What are the financial implications of unexpected improvements in life expectancy for retirement obligations?
• RQ5 How can stochastic mortality tables support effective risk management and hedging strategies in pension finance?

Key findings

• The stochastic extension of the Lee-Carter model successfully captures the uncertainty in future mortality trends, enabling more accurate risk assessment.
• Systematic mortality risk is found to be material and non-diversifiable, significantly impacting long-term pension liabilities.
• Stochastic mortality projections reveal substantial variation in future life expectancy, with implications for funding adequacy.
• The model provides a practical framework for stress testing pension fund solvency under adverse mortality improvements.
• Quantitative risk measures derived from simulations show that longevity risk can lead to significant funding shortfalls under adverse scenarios.
• The approach enables the development of dynamic hedging strategies to mitigate exposure to systematic mortality risk in retirement portfolios.