  We consider two market designs for a network of prosumers, trading energy:
(i) a centralized design which acts as a benchmark, and (ii) a peer-to-peer
market design. High renewable energy penetration requires that the energy
market design properly handles uncertainty. To that purpose, we consider risk
neutral models for market designs (i), (ii), and their risk-averse
interpretations in which prosumers are endowed with coherent risk measures
reflecting heterogeneity in their risk attitudes. We characterize analytically
risk-neutral and risk-averse equilibrium in terms of existence and uniqueness ,
relying on Generalized Nash Equilibrium and Variational Equilibrium as solution
concepts. To hedge their risk towards uncertainty and complete the market,
prosumers can trade financial contracts. We provide closed form
characterisations of the risk-adjusted probabilities under different market
regimes and a distributed algorithm for risk trading mechanism relying on the
Generalized potential game structure of the problem. The impact of risk
heterogeneity and financial contracts on the prosumers' expected costs are
analysed numerically in a three node network and the IEEE 14-bus network.
