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

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Document pages: 31 pages

Abstract: 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.

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