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Optimal Central Bank intervention in the foreign exchange market. (English) Zbl 0998.91041

This paper studies the problem of optimally controlling an exchange rate to keep it close to a given target. There are both a running cost for deviations from the target and fixed and proportional costs for each intervention. The controlled process behaves like a geometric Brownian motion between interventions which are of impulse control type. The authors show how to construct an optimal control from a solution of the quasi-variational inequalities for this problem, construct a solution to the quasi-variational inequalities and numerically provide some comparative statics.

MSC:

91B64 Macroeconomic theory (monetary models, models of taxation)
93E20 Optimal stochastic control
49J40 Variational inequalities
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