Abstract: I will discuss stochastic optimal control problems with model uncertainty either in the form of a discrete sequence of random time horizons or in the form of a parametric dependence on a certain switching process. Such problems are interesting not only for their mathematical novelty, but also for their potential application to subjects such as Finance, Actuarial Science, Economics, Population Dynamics and Engineering. I will focus mainly on the derivation of generalized dynamic programming principles, as well as of the corresponding Hamilton-Jacobi-Bellman equations. Time allowing, I will discuss some applications of these abstract results.