Inter and intra-generational fairness for public pension systems in multi-population mortality models

As populations age, ensuring the sustainability and fairness of pension systems is increasingly crucial. This paper introduces in a pay-as-you-go (PAYG) the Progressive Defined Musgrave (PDM) system, which combines intergenerational and intragenerational adjustment mechanisms. The system aims at long-term financial stability while promoting fairness by addressing disparities in both longevity and income. Intergenerational fairness is maintained through the Musgrave mechanism, which balances economic risks between workers and retirees. Meanwhile, intragenerational fairness is achieved through a progressive pension benefit formula, offering higher replacement rates for lower-income individuals and lower rates for higher-income individuals. The system adapts to changing demographic and economic conditions by adjusting contribution rates and pension benefits annually. The paper explores the mathematical models underlying this design, including multi-population mortality models that capture longevity inequality. Finally, risk analysis using Value-at-Risk demonstrates the adaptability of the PDM system in ensuring financial sustainability and fairness in the face of evolving demographic dynamics.