Time-consistent pension policy with minimum guarantee and sustainability constraint

Abstract

This paper proposes and investigates an optimal pair investment/pension policy for a pay-as-you-go (P A Y G) pension scheme. The social planner can invest in a buffer fund in order to guarantee a minimal pension amount. The model aims at taking into account complex dynamic phenomena such as the demographic risk and its evolution over time, the time and age dependence of agents preferences, and financial risks. The preference criterion of the social planner is modeled by a consistent dynamic utility defined on a stochastic domain, which incorporates the heterogeneity of overlapping generations and its evolution over time. The preference criterion and the optimization problem also incorporate sustainability, adequacy and fairness constraints. The paper designs and solves the social planner’s dynamic decision criterion, and computes the optimal investment/pension policy in a general framework. A detailed analysis for the case of dynamic power utilities is provided.

Keywords

Consistent dynamic utility / P A Y G pension policy / Sustainability and actuarial fairness / Demographic and financial risk sharing / Stochastic control

Acknowledgements

This work is with the financial support of Europlace Institute of Finance (EIF) for the project “Intergenerational risk sharing in pension plans ”. The authors’s research is part of the ANR project DREAMeS (ANR-21-CE46-0002). The research of Sarah Kaakai is Funded by the European Union (ERC, SINGER, 101054787). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them.

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