A model for the optimal management of inflation / Salvatore Federico, Giorgio Ferrari and Patrick Schuhmann
VerfasserFederico, Salvatore In der Gemeinsamen Normdatei der DNB nachschlagen ; Ferrari, Giorgio In der Gemeinsamen Normdatei der DNB nachschlagen ; Schuhmann, Patrick
ErschienenBielefeld, Germany : Center for Mathematical Economics (IMW), Bielefeld University, September 2019
Elektronische Ressource
Umfang1 Online-Ressource (27 Seiten)
SerieCenter for Mathematical Economics Working papers ; 624
URNurn:nbn:de:hbz:6:2-121946 Persistent Identifier (URN)
 Das Dokument ist frei verfügbar.
A model for the optimal management of inflation [0.49 mb]

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.