Before revision:  Based on the this decomposition , we further show that the associated optimal exercise boundary exists , and is a strictly increasing and smooth curve . We also analyze its asymptotic behavior for both large maturity and small time lag using the free-boundary method .
After revision:  Based on the this decomposition , we further show that the associated optimal exercise boundary exists , and is a strictly increasing and smooth curve , and analyze the asymptotic behavior of the value function and the optimal exercise boundary for both large maturity and small time lag using the free-boundary method .