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We consider a government that aims at reducing the debt-to-gross domesticproduct (GDP) ratio of a country. The government observes the level of thedebt-to-GDP ratio and an indicator of the state of the economy, but does notdirectly observe the development of the underlying macroeconomic conditions.The government's criterion is to minimize the sum of the total expected costsof holding debt and of debt's reduction policies. We model this problem as asingular stochastic control problem under partial observation. The contributionof the paper is twofold. Firstly, we provide a general formulation of the modelin which the level of debt-to-GDP ratio and the value of the macroeconomicindicator evolve as a diffusion and a jump-diffusion, respectively, withcoefficients depending on the regimes of the economy. These are describedthrough a finite-state continuous-time Markov chain. We reduce via filteringtechniques the original problem to an equivalent one with full information (theso-called separated problem), and we provide a general verification result interms of a related optimal stopping problem under full information. Secondly,we specialize to a case study in which the economy faces only two regimes, andthe macroeconomic indicator has a suitable diffusive dynamics. In this settingwe provide the optimal debt reduction policy. This is given in terms of thecontinuous free boundary arising in an auxiliary fully two-dimensional optimalstopping problem.

Optimal Reduction of Public Debt under Partial Observation of the Economic Growth