TY  - GEN
AB  - 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.
DA  - 2019
KW  - singular stochastic control
KW  - Dynkin game
KW  - viscosity solution
KW  - free boundary
KW  - smooth-fit
KW  - inflation rate
KW  - interest rate
LA  - eng
PY  - 2019
SN  - 0931-6558
TI  - A Model for the Optimal Management of Inflation
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29376370
Y2  - 2024-11-22T03:24:15
ER  -