Controlling public debt without forgetting Inflation

Ferrari G (2016) Center for Mathematical Economics Working Papers; 564.
Bielefeld: Center for Mathematical Economics.

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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.
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Ferrari G. Controlling public debt without forgetting Inflation. Center for Mathematical Economics Working Papers. Vol 564. Bielefeld: Center for Mathematical Economics; 2016.
Ferrari, G. (2016). Controlling public debt without forgetting Inflation (Center for Mathematical Economics Working Papers, 564). Bielefeld: Center for Mathematical Economics.
Ferrari, G. (2016). Controlling public debt without forgetting Inflation. Center for Mathematical Economics Working Papers, 564, Bielefeld: Center for Mathematical Economics.
Ferrari, G., 2016. Controlling public debt without forgetting Inflation, Center for Mathematical Economics Working Papers, no.564, Bielefeld: Center for Mathematical Economics.
G. Ferrari, Controlling public debt without forgetting Inflation, Center for Mathematical Economics Working Papers, vol. 564, Bielefeld: Center for Mathematical Economics, 2016.
Ferrari, G.: Controlling public debt without forgetting Inflation. Center for Mathematical Economics Working Papers, 564. Center for Mathematical Economics, Bielefeld (2016).
Ferrari, Giorgio. Controlling public debt without forgetting Inflation. Bielefeld: Center for Mathematical Economics, 2016. Center for Mathematical Economics Working Papers. 564.
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