OPTIMAL CONTROL OF DEBT-TO-GDP RATIO IN AN N-STATE REGIME SWITCHING ECONOMY

Ferrari G, Rodosthenous N (2020)
SIAM JOURNAL ON CONTROL AND OPTIMIZATION 58(2): 755-786.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Ferrari, GiorgioUniBi; Rodosthenous, Neofytos
Abstract / Bemerkung
We solve an infinite time-horizon bounded-variation stochastic control problem with regime switching between N states. This is motivated by the problem of a government that wants to control the country's debt-to-GDP (gross domestic product) ratio. In our formulation, the debtto-GDP ratio evolves stochastically in continuous time, and its drift givenby the interest rate on government debt, net of the growth rate of GDP-is affected by an exogenous macroeconomic risk process modelled by a continuous-time Markov chain with N states. The government can act on the public debt by increasing or decreasing its level, and it aims at minimizing a net expected regime-dependent cost functional. Without relying on a guess-and-verify approach, but performing a direct probabilistic study, we show that it is optimal to keep the debt-to-GDP ratio in an interval, whose boundaries depend on the states of the risk process. These boundaries are given through a zero-sum optimal stopping game with regime switching with N states and are characterized through a system of nonlinear algebraic equations with constraints. To the best of our knowledge, such a result appears here for the first time. Finally, we put in practice our methodology in a case study of a Markov chain with N = 2 states; we provide a thorough analysis and we complement our theoretical results by a detailed numerical study on the sensitivity of the optimal debt ratio management policy with respect to the problem's parameters.
Stichworte
singular stochastic control; zero-sum optimal stopping game; free-boundary problem; regime switching; debt-to-GDP ratio
Erscheinungsjahr
2020
Zeitschriftentitel
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
Band
58
Ausgabe
2
Seite(n)
755-786
ISSN
0363-0129
eISSN
1095-7138
Page URI
https://pub.uni-bielefeld.de/record/2944790

Zitieren

Ferrari G, Rodosthenous N. OPTIMAL CONTROL OF DEBT-TO-GDP RATIO IN AN N-STATE REGIME SWITCHING ECONOMY. SIAM JOURNAL ON CONTROL AND OPTIMIZATION. 2020;58(2):755-786.
Ferrari, G., & Rodosthenous, N. (2020). OPTIMAL CONTROL OF DEBT-TO-GDP RATIO IN AN N-STATE REGIME SWITCHING ECONOMY. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 58(2), 755-786. doi:10.1137/19M1245049
Ferrari, G., and Rodosthenous, N. (2020). OPTIMAL CONTROL OF DEBT-TO-GDP RATIO IN AN N-STATE REGIME SWITCHING ECONOMY. SIAM JOURNAL ON CONTROL AND OPTIMIZATION 58, 755-786.
Ferrari, G., & Rodosthenous, N., 2020. OPTIMAL CONTROL OF DEBT-TO-GDP RATIO IN AN N-STATE REGIME SWITCHING ECONOMY. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 58(2), p 755-786.
G. Ferrari and N. Rodosthenous, “OPTIMAL CONTROL OF DEBT-TO-GDP RATIO IN AN N-STATE REGIME SWITCHING ECONOMY”, SIAM JOURNAL ON CONTROL AND OPTIMIZATION, vol. 58, 2020, pp. 755-786.
Ferrari, G., Rodosthenous, N.: OPTIMAL CONTROL OF DEBT-TO-GDP RATIO IN AN N-STATE REGIME SWITCHING ECONOMY. SIAM JOURNAL ON CONTROL AND OPTIMIZATION. 58, 755-786 (2020).
Ferrari, Giorgio, and Rodosthenous, Neofytos. “OPTIMAL CONTROL OF DEBT-TO-GDP RATIO IN AN N-STATE REGIME SWITCHING ECONOMY”. SIAM JOURNAL ON CONTROL AND OPTIMIZATION 58.2 (2020): 755-786.

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