abstract: The trading activity in Intra-Day (ID) electricity market has increased significantly over the last years. We study the problem of a financial agent wishing to maximize the expected utility of hisher terminal wealth when heshe operates in the ID market. Assuming that the price of traded hours follow an additive Ornstein-Uhlenbeck process, we derive the optimal strategy via the Hamilton-Jacobi-Bellman equation. In order to implement it, it is necessary to estimate the model parameters, and one cannot resort to known results, as the typical time series is unevenly time-spaced, with more and more transactions as the maturity approaches. We thus present an estimation procedure for unevenly spaced observations, based on maximum likelihood and a bootstrap bias correction to compensate the few observations at the beginning of the observation frame. Finally, we present a backtest and conclude.