We investigate equilibrium problems arising in a decentralized electricity market involving risk-averse prosumers. The prosumers have the possibility to hedge their risks through financial contracts that they can purchase from an insurance company or trade directly with their peers. We formulate the problem as a Stackelberg game where the insurance company acts as the leader while the prosumers behave as followers. We consider two designs of the problem, in the first model only the insurance company acts as a source of risk-hedging contracts, in the second model we supplement the former design by allowing inter-agent risk-hedging. We derive risk-hedging pricing scheme in each design and show that the Stackelberg game pessimistic formulation might have no solution. We propose an equivalent reformulation as a parametrized generalized Nash equilibrium problem, and characterize the set of equilibria. We prove that the insurance company can design price incentives that guarantee the existence of a solution of the pessimistic formulation, which is ε close to the optimistic one. We then derive economic properties of the Stackelberg equilibria such as fairness, equity, and economic efficiency. We also quantify the impact of the insurance company incomplete information on the prosumers’ risk-aversion levels on its individual cost and social cost. Finally, we evaluate numerically the proposed risk-hedging market models, using residential data provided by Pecan Street.