Finite-horizon optimal stopping, obstacle problems and the shape of the continuation region
Saul Jacka, James R. Lynn · Stochastics and stochastics reports · 1992
We consider the application of probabilistic techniques to an optimal stopping problem, which we write as an obstacle problem. An application of Itô's formula to the optimal payoff function yields a partial uniqueness result for the obstacle problem and for an integral equation satisfied by the continuation region of the stopping problem. We also given sufficient conditions for the continuation region to be of a simple shape