Optimal Reduction of Public Debt under Partial Observation of the Economic Growth
Callegaro G, Ceci C, Ferrari G (2019) Center for Mathematical Economics Working Papers; 608.
Bielefeld: Center for Mathematical Economics.
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| Veröffentlicht | Englisch
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Autor*in
Callegaro, Giorgia;
Ceci, Claudia;
Ferrari, GiorgioUniBi
Abstract / Bemerkung
We consider a government that aims at reducing the debt-to-gross domestic product
(GDP) ratio of a country. The government observes the level of the debt-to-GDP ratio and an
indicator of the state of the economy, but does not directly observe the development of the underlying
macroeconomic conditions. The government's criterion is to minimize the sum of the total expected
costs of holding debt and of debt's reduction policies. We model this problem as a singular stochastic
control problem under partial observation. The contribution of the paper is twofold. Firstly, we
provide a general formulation of the model in which the level of debt-to-GDP ratio and the value of
the macroeconomic indicator evolve as a diffusion and a jump-diffusion, respectively, with coefficients
depending on the regimes of the economy. These are described through a finite-state continuous-time
Markov chain. We reduce via filtering techniques the original problem to an equivalent one with full
information (the so-called separated problem), and we provide a general verification result in terms of
a related optimal stopping problem under full information. Secondly, we specialize to a case study in
which the economy faces only two regimes, and the macroeconomic indicator has a suitable diffusive
dynamics. In this setting we provide the optimal debt reduction policy. This is given in terms of the
continuous free boundary arising in an auxiliary fully two-dimensional optimal stopping problem.
Stichworte
singular stochastic control;
partial observation;
filtering;
separated problem;
optimal stopping;
free boundary;
debt-to-GDP ratio
Erscheinungsjahr
2019
Serientitel
Center for Mathematical Economics Working Papers
Band
608
ISSN
0931-6558
Page URI
https://pub.uni-bielefeld.de/record/2933360
Zitieren
Callegaro G, Ceci C, Ferrari G. Optimal Reduction of Public Debt under Partial Observation of the Economic Growth. Center for Mathematical Economics Working Papers. Vol 608. Bielefeld: Center for Mathematical Economics; 2019.
Callegaro, G., Ceci, C., & Ferrari, G. (2019). Optimal Reduction of Public Debt under Partial Observation of the Economic Growth (Center for Mathematical Economics Working Papers, 608). Bielefeld: Center for Mathematical Economics.
Callegaro, Giorgia, Ceci, Claudia, and Ferrari, Giorgio. 2019. Optimal Reduction of Public Debt under Partial Observation of the Economic Growth. Vol. 608. Center for Mathematical Economics Working Papers. Bielefeld: Center for Mathematical Economics.
Callegaro, G., Ceci, C., and Ferrari, G. (2019). Optimal Reduction of Public Debt under Partial Observation of the Economic Growth. Center for Mathematical Economics Working Papers, 608, Bielefeld: Center for Mathematical Economics.
Callegaro, G., Ceci, C., & Ferrari, G., 2019. Optimal Reduction of Public Debt under Partial Observation of the Economic Growth, Center for Mathematical Economics Working Papers, no.608, Bielefeld: Center for Mathematical Economics.
G. Callegaro, C. Ceci, and G. Ferrari, Optimal Reduction of Public Debt under Partial Observation of the Economic Growth, Center for Mathematical Economics Working Papers, vol. 608, Bielefeld: Center for Mathematical Economics, 2019.
Callegaro, G., Ceci, C., Ferrari, G.: Optimal Reduction of Public Debt under Partial Observation of the Economic Growth. Center for Mathematical Economics Working Papers, 608. Center for Mathematical Economics, Bielefeld (2019).
Callegaro, Giorgia, Ceci, Claudia, and Ferrari, Giorgio. Optimal Reduction of Public Debt under Partial Observation of the Economic Growth. Bielefeld: Center for Mathematical Economics, 2019. Center for Mathematical Economics Working Papers. 608.
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