TY - JOUR
TI - Optimal Foreign Exchange Rate Intervention in Lévy Markets
VL - 2014
PY - 2014
DA - 2014/11/26
DO - 10.1155/2014/746815
UR - https://doi.org/10.1155/2014/746815
AB - This paper considers an exchange rate problem in Lévy markets, where the Central Bank has to intervene. We assume that, in the absence of control, the exchange rate evolves according to Brownian motion with a jump component. The Central Bank is allowed to intervene in order to keep the exchange rate as close as possible to a prespecified target value. The interventions by the Central Bank are associated with costs. We present the situation as an impulse control problem, where the objective of the bank is to minimize the intervention costs. In particular, the paper extends the model by Huang, 2009, to incorporate a jump component. We formulate and prove an optimal verification theorem for the impulse control. We then propose an impulse control and construct a value function and then verify that they solve the quasivariational inequalities. Our results suggest that if the expected number of jumps is high the Central Bank will intervene more frequently and with large intervention amounts hence the intervention costs will be high.
JF - International Journal of Stochastic Analysis
SN - 2090-3332
PB - Hindawi Publishing Corporation
SP - 746815
KW -
A2 - Sulem, Agnès
AU - Mutakaya, Masimba Aspinas
AU - Chikodza, Eriyoti
AU - Chiyaka, Edward T.
ER -