Controlling public debt without forgetting inflation - Giorgio Ferrari (Bielefeld University, Center for Mathematical Economics (IMW), 2016)
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.
urn:nbn:de:0070-pub-29047501
Keywords: C61; H63; 330; debt-to-GDP ratio; inflation rate; debt ceiling; singular stochastic control; optimal stopping; free-boundary; nonlinear integral equation