@techreport{2904750,
abstract = {Consider the problem of a government that wants to control its debt-to-GDP
(gross domestic product) ratio, while taking into consideration the evolution of the inflation
rate of the country. The uncontrolled inflation rate follows an Ornstein-Uhlenbeck dynamics
and affects the growth rate of the debt ratio. The level of the latter can be reduced by the
government through fiscal interventions. The government aims at choosing a debt reduction
policy which minimises the total expected cost of having debt, plus the total expected cost of
interventions on debt ratio. We model such problem as a two-dimensional singular stochastic
control problem over an infinite time-horizon. We show that it is optimal for the government
to adopt a policy that keeps the debt-to-GDP ratio under an inflation-dependent ceiling. This
curve is the free-boundary of an associated fully two-dimensional optimal stopping problem, and
it is shown to be the unique solution of a nonlinear integral equation.},
author = {Ferrari, Giorgio},
issn = {0931-6558},
keyword = {debt-to-GDP ratio, inflation rate, debt ceiling, singular stochastic control, optimal stopping, free-boundary, nonlinear integral equation},
pages = {33},
publisher = {Center for Mathematical Economics},
title = {{Controlling public debt without forgetting Inflation}},
volume = {564},
year = {2016},
}