Abstract:
This paper is concerned with the optimal stopping problem for Itô
diffusion processes over a class of stopping times. Necessary and sufficient optimality
conditions are studied for a parametrically
specified class of stopping times. A detailed analysis is given for the case of
one-dimensional diffusion processes and threshold stopping times. Necessary
and sufficient conditions are put forward for optimality of
a threshold stopping time over
all stopping times. A number of relations are obtained between the
solution of the optimal stopping problem over the class of threshold moments
and the solution of the free-boundary problem.
Keywords:diffusion processes, optimal stopping, threshold stopping time, free-boundary problem.
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