Optimal Control of Debt-To-GDP Ratio in an N-State Regime Switching Economy

Ferrari G, Rodosthenous N (2019) Center for Mathematical Economics Working Papers; 589, Aktual. Version Februar 2019.
Bielefeld: Center for Mathematical Economics.

Diskussionspapier | Veröffentlicht | Englisch
 
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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 debt-to-GDP ratio evolves stochastically in continuous time, and its drift - given by 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 minimising a net expected 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 we completely characterise them as solutions to 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
2019
Band
589
ISSN
0931-6558
Page URI
https://pub.uni-bielefeld.de/record/2933813

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Ferrari G, Rodosthenous N. Optimal Control of Debt-To-GDP Ratio in an N-State Regime Switching Economy. Center for Mathematical Economics Working Papers. Vol 589 Aktual. Version Februar 2019. Bielefeld: Center for Mathematical Economics; 2019.
Ferrari, G., & Rodosthenous, N. (2019). Optimal Control of Debt-To-GDP Ratio in an N-State Regime Switching Economy (Center for Mathematical Economics Working Papers, 589) Aktual. Version Februar 2019. Bielefeld: Center for Mathematical Economics.
Ferrari, G., and Rodosthenous, N. (2019). Optimal Control of Debt-To-GDP Ratio in an N-State Regime Switching Economy. Center for Mathematical Economics Working Papers, 589, Aktual. Version Februar 2019. Bielefeld: Center for Mathematical Economics.
Ferrari, G., & Rodosthenous, N., 2019. Optimal Control of Debt-To-GDP Ratio in an N-State Regime Switching Economy, Center for Mathematical Economics Working Papers, no.589, Aktual. Version Februar 2019., Bielefeld: Center for Mathematical Economics.
G. Ferrari and N. Rodosthenous, Optimal Control of Debt-To-GDP Ratio in an N-State Regime Switching Economy, Center for Mathematical Economics Working Papers, vol. 589, Aktual. Version Februar 2019., Bielefeld: Center for Mathematical Economics, 2019.
Ferrari, G., Rodosthenous, N.: Optimal Control of Debt-To-GDP Ratio in an N-State Regime Switching Economy. Center for Mathematical Economics Working Papers, 589, Aktual. Version Februar 2019. Center for Mathematical Economics, Bielefeld (2019).
Ferrari, Giorgio, and Rodosthenous, Neofytos. Optimal Control of Debt-To-GDP Ratio in an N-State Regime Switching Economy. Aktual. Version Februar 2019. Bielefeld: Center for Mathematical Economics, 2019. Center for Mathematical Economics Working Papers. 589.
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