Cloud computing has become the leading paradigm for deploying large-scale infrastructures and running big data applications, due to its capacity of achieving economies of scale. In this work, we focus on one of the most prominent advantages of cloud computing, namely the on-demand resource provisioning, which is commonly referred to as elasticity. Although a lot of effort has been invested in developing systems and mechanisms that enable elasticity, the elasticity decision policies tend to be designed without guaranteeing or quantifying the quality of their operation. This work aims to make the development of elasticity policies more formalized and dependable. We make two distinct contributions. First, we propose an extensible approach to enforcing elasticity through the dynamic instantiation and online quantitative verification of Markov Decision Processes (MDP) using probabilistic model checking. Second, we propose concrete elasticity models and related elasticity policies. We evaluate our decision policies using both real and synthetic datasets in clusters of NoSQL databases. According to the experimental results, our approach improves upon the state-of-the-art in significantly increasing user-defined utility values and decreasing user-defined threshold violations.