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10.5. EVENTUAL COLLAPSE 3210.03s0.02s=f0.010-0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02 0.025-0.01G(f)f-0.02-0.03Figure 10.2: Exchange rate and fundamentals under Flood—Garber discreteinterventionsexchange rate regime operating under a discrete intervention rule, onthe other hand, must eventually collapse. The central bank begins theregime with a Þnite amount of reserves which is eventually exhausted.This is a variant of the gambler’s ruin problem. 7The problem that confronts the central bank goes like this. Supposethe authorities begin with foreign exchange reserves of R dollars. Itloses one dollar each time ¯f is hit and gains one dollar each time f ishit. After the intervention, f is placed back in the middle of the [f, ¯f]band, where it evolves according to the driftless diffusion df (t) =σdz(t)until another intervention is required.Let L be the event that central bank eventually runs out of reserves,G be the event that it gains $1 on a particular intervention and G c be7 See Degroot [37].