  The problem of detecting a change in the drift of a Brownian motion is
considered. The change point is assumed to have a modified exponential prior
distribution with unknown parameters. A worst-case analysis with respect to
these parameters is adopted leading to a min-max problem formulation.
Analytical and numerical justifications are provided towards establishing that
the Shiryaev-Roberts procedure with a specially designed starting point is
exactly optimal for the proposed mathematical setup.
