Before revision:  It permits to recover the well-known results of Karatzas and Zhao in the case of conjugate (Gaussian) priors for the drift distribution  , but also to go beyond the no-friction case, when martingale methods are no longer available.
After revision:  It permits to recover the well-known results of Karatzas and Zhao in the case of conjugate (Gaussian) priors for the drift distribution Merton , but also to go beyond the no-friction case, when martingale methods are no longer available.