  We introduce a non-Markovian model for electricity markets where the spot
price of electricity is driven by several Gaussian Volterra processes, which
can be e.g., fractional Brownian motions (fBms), Riemann-Liouville processes or
Gaussian-Volterra driven Ornstein-Uhlenbeck processes. Since in energy markets
the spot price is not a tradeable asset, due to the limited storage
possibilities, forward contracts are considered as traded products. We ensure
necessary and sufficient conditions for the absence of arbitrage that, in this
kind of market, reflects the fact that the prices of the forward contracts are
(Gaussian) martingales under a risk-neutral measure. Moreover, we characterize
the market completeness in terms of the number of forward contracts
simultaneously considered and of the kernels of the Gaussian-Volterra
processes. Then, we formulate a portfolio optimization problem for an agent who
invests in an electricity market, and we solve it explicitly in the case of
CRRA utility functions. We also find closed formula for the price of options
written on forward contracts, together with the hedging strategy. Finally, we
provide a novel representation of Ornstein-Uhlenbeck (OU) processes driven by
Gaussian Volterra processes. Also exploiting this result, we show analytically
that, for some kinds of Gaussian-Volterra processes driving the spot prices,
under conditions ensuring the absence of arbitrage, the market is complete.
