Orateur
Description
ABSTRACT: We consider the problem faced by a Central Bank of optimally
controlling the exchange rate over a finite time horizon, whereby it can use
two non-excluding tools: controlling directly the exchange rate in the
form of an impulse control; controlling it indirectly via the domestic
exchange rate in the form of a continuously acting control. In line
with existing literature we consider this as a mixed
classical-impulse control problem for which, on the basis of a
quasi-variational inequality, we search for an analytic solution within a
specific class of value functions and controls. Besides the finite
horizon, the main novelty here is the assumption that the drift in the
exchange rate dynamics is not directly observable and has thus to be
filter-estimated from observable data. The problem becomes thus time
inhomogeneous and the Markovian state variables have to include also
the filter of the drift. This is a joint work with
Kazuhiro Yasuda.
