On the optimal stopping of a one-dimensional diffusion. (English) Zbl 1296.60101

The authors study a one-dimensional diffusion based optimal stopping problem. On the one hand, the authors aim to derive a simple necessary and sufficient condition such that the value function is the difference of two convex functions and satisfies a variational inequality. On the other hand, the authors derive a simple necessary and sufficient condition for a solution to this variational inequality to identify with the value function. Some related characterizations such as “principle of smooth fit” of the solution to the optimal problem are also established.


60G40 Stopping times; optimal stopping problems; gambling theory
60J55 Local time and additive functionals
60J60 Diffusion processes
49L20 Dynamic programming in optimal control and differential games
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