A Free Boundary Problem Connected with the Optimal Stopping Problem for Diffusion Processes
Daniel B. Kotlow · Transactions of the American Mathematical Society · 1973
This paper deals with a free boundary problem for a parabolic equation in one space variable which arises from the problem of selecting an optimal stopping strategy for the diffusion process connected with the equation. It is shown that a solution of the free boundary problem yields the solution of a minimum problem concerning supersolutions of the parabolic equation as well as the solution of the optimal stopping problem. Theorems regarding the existence, uniqueness, regularity, and approach to the steady state of solutions of the free boundary problem are established.