Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/227820
Year of Publication: 
2019
Series/Report no.: 
Center for Mathematical Economics Working Papers No. 624
Publisher: 
Bielefeld University, Center for Mathematical Economics (IMW), Bielefeld
Abstract: 
Consider a central bank that can adjust the in ation rate by increasing and decreasing the level of the key interest rate. Each intervention gives rise to proportional costs, and the central bank faces also a running penalty, e.g., due to misaligned levels of in ation and interest rate. We model the resulting minimization problem as a Markovian degenerate two-dimensional bounded-variation stochastic control problem. Its characteristic is that the mean-reversion level of the diffusive in ation rate is an affine function of the purely controlled interest rate's current value. By relying on a combination of techniques from viscosity theory and free-boundary analysis, we provide the structure of the value function and we show that it satisfies a second-order smooth-fit principle. Such a regularity is then exploited in order to determine a system of functional equations solved by the two monotone curves that split the control problem's state space in three connected regions.
Subjects: 
singular stochastic control
Dynkin game
viscosity solution
free boundary
smooth-fit
inflation rate
interest rate
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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