A critical review of stochastic control approaches in government debt management

This paper provides a comprehensive and critical review of the literature on stochastic control methods applied to sovereign debt management. In the face of increasing economic uncertainty and fiscal constraints, stochastic control theory has emerged as a powerful framework for modeling the dynamics of the debt-to-GDP ratio and designing optimal fiscal policies. We present an overview of existing models based on their methodological foundations, spanning from deterministic benchmarks to advanced stochastic formulations that account for multiple sources of randomness and partial information. The review highlights key theoretical contributions, including the use of dynamic programming, Hamilton–Jacobi–Bellman (HJB) equations, HJB-variational equations and filtering techniques which are applied in partial information frameworks. We compare models across different controlled dynamics for the debt-to-GDP ratio, objective functionals, information structures, and policy implications. Moreover, we highlight some areas where further refinement could enhance current approaches, including assumptions, empirical calibration, and interpretability. Finally, we suggest promising avenues for future research, focusing on models that combine endogenous growth, robust fiscal policy design, and advanced mathematical techniques.