—Since video traffic has become the major source of generated mobile traffic worldwide, there has been a strong interest in new techniques to improve the Quality of Experience (QoE) of users generating this traffic. Several efforts have been made to propose adaptive streaming algorithms on the client side to be able to adjust the quality of the downloaded video segments to the current network conditions, taking advantage of the Dynamic Adaptive Streaming over HTTP (DASH) standard. This study uses this knowledge to propose a pre-fetching proxy cache, to be placed at the network's edge, which will predict the quality that the client will request for the following segment. The proxy predicts the future network conditions and models the system as a Markov Decision Process (MDP), in order to find the optimal decision for the proxy, given the current network conditions. This Just-in-Time caching technique pre-fetches the segment just before the client requests it, aiming to decrease the total time spent by the client downloading the segments, and indirectly increasing the user's QoE, as the DASH client will perceive better network conditions. The study concludes that the predictive technique improves QoE by increasing the video quality and decreasing the number of stalling events, in comparison to solutions that pre-fetch the previously requested quality, and solutions which do not use any pre-fetching technique.