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We describe a variational approach to solving optimal stopping problems fordiffusion processes, as an alternative to the traditional approach based on thesolution of the free-boundary problem. We study smooth pasting conditions froma variational point of view, and give some examples when the solution tofree-boundary problem is not the solution to optimal stopping problem. Aspecial attention is paid to threshold strategies which allow reduce optimalstopping problem to more simple one-parametric optimization. Necessary andsufficient conditions for threshold structure of optimal stopping time arederived. We apply these results to both investment timing and optimal abandonmodels.

Variational View to Optimal Stopping Problems for Diffusion Processes and Threshold Strategies