Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/149021
Authors: 
Ferrari, Giorgio
Year of Publication: 
2016
Series/Report no.: 
Working Papers, Center for Mathematical Economics 564
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.
Subjects: 
debt-to-GDP ratio
inflation rate
debt ceiling
singular stochastic control
optimal stopping
free-boundary
nonlinear integral equation
JEL: 
C61
H63
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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