•A decentralized energy trading algorithm is proposed considering the integration of renewable energy resources.•Our method optimizes the cost of load aggregators and profit of the generators.•The proposed optimization problem minimizes as the risk of shortage in the renewable generation.•A risk measure called the conditional-value-at-risk (CVaR) is used to model uncertainty of renewables.•The simulation results validate the effectiveness of the proposed decentralized algorithm. The uncertainties in renewable power generators and the proliferation of price-responsive load aggregators make it a challenge for independent system operators (ISOs) to manage the energy trading in the power markets. Hence, a centralized framework for the energy trading market may not be remained practical for the ISOs mainly due to violating the privacy of different entities, i.e., load aggregators and generators. It can also suffer from the high computational burden in a market with a large number of entities. Instead, in this paper, we focus on proposing a decentralized energy trading framework enabling the ISO to incentivize the entities toward an operating point that jointly optimize the cost of load aggregators and profit of the generators, as well as the risk of shortage in the renewable generation. To address the uncertainties in the renewable resources, we apply a risk measure called the conditional value-at-risk (CVaR) with the goal of limiting the likelihood of high renewable generation shortage with a certain confidence level. Then by considering the risk attitude of the ISO and the generators, we develop a decentralized energy trading algorithm with some control signals that properly coordinate the entities toward the market operating point of the ISO’s centralized approach. Simulation results on the IEEE 30-bus test system show that the proposed decentralized algorithm converges to the solution of the ISO’s centralized problem in a timely fashion. Furthermore, the load aggregators can help their consumers reduce their electricity cost by 18% on average through managing their loads using locally available information. Meanwhile, the generators can benefit from 17.1% increase in their total profit through decreasing their generation cost.