A novel model-based approach to 3D hand tracking from monocular video is presented. The 3D hand pose, the hand texture and the illuminant are dynamically estimated through minimization of an objective function. Derived from an inverse problem formulation, the objective function enables explicit use of texture temporal continuity and shading information, while handling important self-occlusions and time-varying illumination. The minimization is done efficiently using a quasi-Newton method, for which we propose a rigorous derivation of the objective function gradient. Particular attention is given to terms related to the change of visibility near self-occlusion boundaries that are neglected in existing formulations. In doing so we introduce new occlusion forces and show that using all gradient terms greatly improves the performance of the method. Experimental results demonstrate the potential of the formulation.