Proactive caching holds the promise of coping with the explosively increasing traffic demands of next generation mobile networks. However, it may also incur extra pushing and storage costs for base stations (BSs). By taking these costs into account, we are interested in maximizing the average profit for the BS. A joint pushing and caching (JPC) approach is investigated to determine whether and when to push and how long a file should be cached at the user's buffer. More specifically, we present a dynamic programming based JPC for the BS that knows the distributions of user's request times for content files. When user's request time distributions are unknown in priori, we adopt a reinforcement learning algorithm to achieve high bandwidth and storage efficiency.