  We study an optimal portfolio problem designed for an agent operating in
intraday electricity markets. The investor is allowed to trade in a single
risky asset modelling the continuously traded power and aims to maximize the
expected terminal utility of his wealth. We assume a mean-reverting additive
process to drive the power prices. In the case of logarithmic utility, we
reduce the fully non-linear Hamilton-Jacobi-Bellman equation to a linear
parabolic integro-differential equation, for which we explicitly exhibit a
classical solution in two cases of modelling interest. The optimal strategy is
given implicitly as the solution of an integral equation, which is possible to
solve numerically as well as to describe analytically. An analysis of two
different approximations for the optimal policy is provided. Finally, we
perform a numerical test by adapting the parameters of a popular electricity
spot price model.
