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Optimal stopping of Brownian motion with broken drift
We solve an optimal stopping problem where the underlying diffusion is
Brownian motion on with a positive drift changing at zero. It is
assumed that the drift on the negative side is smaller than the drift
on the positive side. The main observation is that if
then there exists values of the discounting parameter for which it is not
optimal to stop in the vicinity of zero where the drift changes. However, when
the discounting gets bigger the stopping region becomes connected and contains
zero. This is in contrast with results concerning optimal stopping of skew
Brownian motion where the skew point is for all values of the discounting
parameter in the continuation region.Comment: 12 pages, 2 figure