Before revision:  Our setup captures the position of an executive (insider) and employee (outsider), who receive executive stock options. The latter yields a model under the observation filtration  where the drift process \mathbb{F}  becomes a diffusion driven by the innovations process, an  \mathbb{F} -Brownian motion also driving the stock under  \widehat{\mathbb{F}} , and the partial information optimal stopping problem has two spatial dimensions.
After revision:  This scenario is designed to mimic the positions of two employees of varying seniority, a fully informed executive and a partially informed less senior employee, each of whom receives an ESO. The partial information scenario yields a model under the observation filtration  where the drift process \mathbb{F} becomes a diffusion driven by the innovations process, an  \mathbb{F} -Brownian motion also driving the stock under  \widehat{\mathbb{F}} , and the partial information optimal stopping problem has two spatial dimensions.