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Smart Grid is expected to support a variety of services for energy prosumers - entities that are able both to produce and consume energy. Enabling cooperation among such prosumers in the form of energy trading may be highly beneficial for all actors in Smart Grid. However, in order to provide energy trading capabilities, a communication infrastructure that will be able to offer energy trading service to a massive number of energy traders dispersed over a large geographic area is needed. In this paper, we argue that a 4G/5G cellular network that offers cellular Internet of Things (IoT) services and provides mobile edge computing (MEC) capabilities is ideally suited for future widespread energy trading. We discuss architecture of such a system, identify and present analytic models for each of its parts that also account for stochastic aspects, and propose an overall energy trading system model. By doing so, we obtain a novel optimization problem formulation of the energy trading, that is capable of handling uncertainties in price changes. Our results and discussion provides initial insights towards the design of energy trading services via emerging IoT/MEC-enabled mobile cellular networks. © 2019 IEEE.