As an extension of (Progress in industrial mathematics at ECMI 2018, pp. 469-475, 2019), this paper is concerned with a new mathematical model for intraday electricity trading involving both renewable and conventional generation. The model allows to incorporate market data e.g. for half-spread and immediate price impact. The optimal trading and generation strategy of an agent is derived as the viscosity solution of a second-order Hamilton-Jacobi-Bellman (HJB) equation for which no closed-form solution can be given. We construct a numerical approximation allowing us to use continuous input data. Numerical results for a portfolio consisting of three conventional units and wind power are provided.

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We use point processes to analyze market order arrivals on the intraday market for hourly electricity deliveries in Germany in the second quarter of 2015. As we distinguish between buys and sells, we work in a multivariate setting. We model the arrivals with a Hawkes process whose baseline intensity comprises either only an exponentially increasing component or a constant in addition to the exponentially increasing component, and whose excitation decays exponentially. Our goodness-of-fit tests indicate that the models where the intensity of each market order type is excited at least by events of the same type are the most promising ones. Based on the Akaike information criterion, the model without a constant in the baseline intensity and only self-excitation is selected in almost 50% of the cases on both market sides. The typical jump size of intensities in case of the arrival of a market order of the same type is quite large, yet rather short lived. Diurnal patterns in the parameters of the baseline intensity and the branching ratio of self-excitation are observable. Contemporaneous relationships between different parameters such as the jump size and decay rate of self and cross-excitation are found.

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