TY  - GEN
AB  - 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.
DA  - 2019
KW  - singular stochastic control
KW  - partial observation
KW  - filtering
KW  - separated problem
KW  - optimal stopping
KW  - free boundary
KW  - debt-to-GDP ratio
LA  - eng
PY  - 2019
SN  - 0931-6558
TI  - Optimal Reduction of Public Debt under Partial Observation of the Economic Growth
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29333605
Y2  - 2024-11-22T10:21:39
ER  -