This talk will be focused on the analytic studies of the Parisi functional and the two- dimensional Guerra-Talagrand (GT) bound in the mixed p-spin model. We will present a new approach, motivated by the theory of optimal stochastic control, to analyzing these two objects. We first compute the directional derivative of the Parisi functional and obtain equivalent criteria for the Parisi measure. Next we demonstrate how our approach provides an efficient control for the GT bound and yield several results on the positivity of the overlap and disorder chaos problem.