Stochastic impulse control of exchange rates with Freidlin–Wentzell perturbations

This paper pioneers a Freidlin–Wentzell approach to stochastic impulse control of exchange rates when the central bank desires to maintain a target zone. Pressure to stimulate the economy forces the bank to implement diffusion monetary policy involving Freidlin–Wentzell perturbations indexed by a parameter ε∈ [0,1]. If ε=0, the policy keeps exchange rates in the target zone for all times t≥0. When ε>0, exchange rates continually exit the target zone almost surely, triggering central bank interventions which force currencies back into the zone or abandonment of all targets. Interventions and target zone deviations are costly, motivating the bank to minimize these joint costs for any ε∈ [0,1]. We prove convergence of the value functions as ε→0 achieving a value function approximation for small ε. Via sample path analysis and cost function bounds, intervention followed by target zone abandonment emerges as the optimal policy.