Salvatore Federico
DEPS, USiena
Giorgio Ferrari
IMW, Bielefeld University
Patrick Schuhmann
IMW, Bielefeld University
Abstract
Consider a central bank that can adjust the inflation 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 inflation 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 inflation 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.
Keywords
singular stochastic control; Dynkin game; viscosity solution; free boundary; smooth-fit; inflation rate; interest rate; central bank policies
Jel Codes
C61, C73, E58.
