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We consider an American put option under the CEV process. This corresponds toa free boundary problem for a PDE. We show that this free bondary satisfies anonlinear integral equation, and analyze it in the limit of small $\rho$ = $2r/\sigma^2$, where $r$ is the interest rate and $\sigma$ is the volatility. Weuse perturbation methods to find that the free boundary behaves differently forfive ranges of time to expiry.

On a free boundary problem for an American put option under the CEV process