The first part of this thesis is concerned with the qualitative behaviour of path dependent stochastic differential equations, specifically equations of functional and Volterra type. We deeply investigate the effects of perturbations on stable linear systems. First, we provide a framework for characterising the solution space of perturbed linear integrodifferential Volterra convolution equations and their finite memory counterpart, namely perturbed linear functional differential equations. This improves upon classical admissibility theory which only provides sufficient conditions on the perturbations to ensure solutions are elements of a particular function space. Next we consider state independent stochastic perturbations and aim to characterise when the sample paths of the solution converge to zero almost surely and when the trajectories are almost surely p-integrable functions in time. We then shift our focus to perturbed equations with multiplicative noise and characterise the asymptotic behaviour of the mean square. Our findings indicate the pointwise behaviour of state independent perturbations is non-dominant and does not necessarily proliferate through to the solution. Rather the main quantity that determines the qualitative behaviour of the solution is a particular functional of the state independent perturbations, namely one must study the integral of the perturbations over compact intervals. It is this insight that leads to sharp characterisations of the qualitative behaviour of solutions. The second part of this thesis is dedicated to a particular class of stochastic control problems arising in finance. We provide a novel approach to the optimal consumption-investment problem which aims to characterise the value function as the solution to an associated variational problem. The utility of this approach is twofold, it circumvents the need to analytically solve the Hamilton-Jacobi-Bellman equation while also providing a new set of tools to analyse the value function. Sharp estimates on the value function and the optimal policies are obtained via analysing the variational problem directly and employing standard techniques from the theory of elliptic partial differential equations.