Optimal foreign exchange rate intervention in Lévy markets
type: Item
instance of: scholarly article
title: Optimal foreign exchange rate intervention in Lévy markets
zbMATH Open document ID: 1321.93064
DOI: 10.1155/2014/746815
author: Masimba Aspinas Mutakaya
author: Eriyoti Chikodza
author: Edward T. Chiyaka
published in: International Journal of Stochastic Analysis
publication date: 2015-03-27T00:00:00Z
review text: Summary: 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 of \textit{H. Huang} [``Optimal Impulse Control in the Foreign Exchange Market'', Paper for PCE (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.
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 91B70
Mathematics Subject Classification ID: 60G40
zbMATH DE Number: 6420151
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/746815
OpenAlex ID: W1985465751
Wikidata QID: Q59047047
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description: scientific article; zbMATH DE number 6420151