Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/288425 
Year of Publication: 
2020
Citation: 
[Journal:] Finance and Stochastics [ISSN:] 1432-1122 [Volume:] 24 [Issue:] 4 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2020 [Pages:] 1083-1132
Publisher: 
Springer, Berlin, Heidelberg
Abstract: 
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 minimise the sum of the total expected costs of holding debt and of debt 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 the 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. The latter are described through a finite-state continuous-time Markov chain. We reduce the original problem via filtering techniques 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 specialise 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.
Subjects: 
Singular stochastic control
Partial observation
Optimal stopping
Free boundary
Debt-to-GDP ratio
JEL: 
E20
G35
E11
G40
J60
B64
C61
H63
E32
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

Files in This Item:
File
Size





Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.