@techreport{Ferrari2019Optimal,
abstract = {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.},
address = {Bielefeld},
author = {Giorgio Ferrari and Neofytos Rodosthenous},
copyright = {http://www.econstor.eu/dspace/Nutzungsbedingungen},
keywords = {330; singular stochastic control; zero-sum optimal stopping game; free-boundary problem; regime switching; debt-to-GDP ratio},
language = {eng},
note = {urn:nbn:de:0070-pub-29338135},
number = {589},
publisher = {Bielefeld University, Center for Mathematical Economics (IMW)},
title = {Optimal control of debt-to-GDP ratio in an N-state regime switching economy},
type = {Center for Mathematical Economics Working Papers},
url = {http://hdl.handle.net/10419/201614},
year = {2019}
}