Faculty of Mathematics
Collaborative Research Centre 701
Spectral Structures and Topological Methods in Mathematics
stripes SFB701

Wednesday, November 15, 2017 - 16:15 in V3-201

Classical and Restricted Impulse Control for the Exchange Rate under Incomplete Knowledge of the Model

A talk in the 'Bielefeld Stochastic Afternoon - Math Finance Session' series by
Wolfgang Runggaldier from University of Padova
Abstract: We consider the problem faced by a Central Bank of optimally controlling the exchange assuming that 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 the existing literature, we consider this as a mixed classical-impulse control problem and, on the basis of a quasi-variational inequality, 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. (Joint with K.Yasuda)