Traffic offloading using opportunistic device-to-device (D2D) communications is a new and exciting opportunity for cellular operators to cope with the unprecedented mobile data growth. A limitation of existing proposals is that they assume that all terminals are, by default, involved in the D2D forwarding process. In particular, they do not capture the need to reward seed users. For this reason, we include a rewarding cost in the design of the opportunistic offloading strategy. In our solution, we make the difference between nodes that receive content through the cellular channel only (leechers) and nodes that take part in the forwarding process (seeders). The key point for an operator is to design a global strategy to select which nodes act as seeders and which ones as leechers, in order to reduce the total dissemination cost. We formulate this question as a stochastic control problem that we solve using an application of Pontryagin's Maximum Principle. We provide a mathematical framework to devise the optimal strategy for opportunistic offloading under a generic cost model. First, we show that an optimal solution exists; then, from this policy, we extract some insights to develop heuristics. Finally, we discuss the advantages of the proposed model compared to the classic seeder-only model. We demonstrate that separating seeders/leechers leads to better incentive strategies in the most demanding cases of content with a large span of delivery delays.