Consider the problem of a government that wants to control the debt-to-GDP (gross domestic product) ratio of a country, while taking into consideration the evolution of the inflation rate. 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 given in terms of the solution of a nonlinear integral equation arising in the study of a fully two-dimensional optimal stopping problem.
On the Optimal Management of Public Debt: a Solvable Two-Dimensional Singular Stochastic Control Problem
Giorgio Ferrari (Uni Bielefeld)
Wed, 24/05/2017 - 13:00