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In this paper, we propose dynamic, short-term, financial risk management strategies for small electricity producers and buyers that trade in the wholesale electricity markets. Since electricity is mostly nonstorable, financial risk coming from extremely volatile electricity prices cannot be reduced by using standard finance-based approaches. Instead, a short-term operational planing and a proper trade diversification might be used. In this paper, we analyze the price risk in terms of the Markowitz mean–variance portfolio theory. Hence, it is crucial to forecast properly the variance of electricity prices. To this end, we jointly model day-ahead and intraday or balancing prices from Germany and Poland using ARX-GARCH type models. We show that using heteroscedastic volatility significantly improves probabilistic price forecasts according to the pinball score, especially if variance stabilizing transformation is applied prior to a model estimation. The price forecasts are then used for construction of dynamic diversification strategies that are based on volatility-type risk measures. We consider different objectives as well as a buyer’s and a seller’s perspective. The proposed strategies are applied for the diversification of trade among different markets in Germany and Poland. We show that the objective of the strategy can be achieved using the proposed approach, but the risk minimization is usually related to lower profits. We find that risk minimization is especially important for a seller in both markets, while for a buyer a profit maximization objective leads to a more optimal risk–return trade-off.

Multivariate modelling of economics data is crucial for risk and profit analyses in companies. However, for the final conclusions, a whole set of variables is usually transformed into a single variable describing a total profit/balance of company’s cash flows. One of the possible transformations is based on the product of market variables. Thus, in this paper, we study the distribution of products of Pareto or Student’s t random variables that are ubiquitous in various risk factors analysis. We review known formulas for the probability density functions and derive their explicit forms for the products of Pareto and Gaussian or log-normal random variables. We also study how the Pareto or Student’s t random variable influences the asymptotic tail behaviour of the distribution of their product with the Gaussian or log-normal random variables and discuss how the dependency between the marginal random variables of the same type influences the probabilistic properties of the final product. The theoretical results are then applied for an analysis of the distribution of transaction values, being a product of prices and volumes, from a continuous trade on the German intraday electricity market.

Diffusion of nanoparticles in the cytoplasm of live cells has frequently been reported to exhibit an anomalous and even heterogeneous character, i.e. particles seem to switch gears during their journey. Here we show by means of a hidden Markov model that individual trajectories of quantum dots in the cytoplasm of living cultured cells feature a dichotomous switching between two distinct mobility states with an overall subdiffusive mode of motion of the fractional Brownian motion (FBM) type. Using the extracted features of experimental trajectories as input for simulations of different variants of a two-state FBM model, we show that the trajectory-intrinsic and the ensemble-wise heterogeneity in the experimental data is mostly due to variations in the (local) transport coefficients, with only minor contributions due to locally varying anomaly exponents. Altogether, our approach shows that diffusion heterogeneities can be faithfully extracted and quantified from fairly short trajectories obtained by single-particle tracking in highly complex media.

In this paper we propose an optimization scheme for a selling strategy of an electricity producer who in advance decides on the share of electricity sold on the day-ahead market. The remaining part is sold on the complementary (intraday/balancing) market. To this end, we use probabilistic forecasts of the future selling price distribution. Next, we find an optimal share of electricity sold on the day-ahead market using one of the three objectives: maximization of the overall profit, minimization of the sellers risk, or maximization of the median of portfolio values. Using data from the Polish day-ahead and balancing markets, we show that the assumed objective is achieved, as compared to the naive strategy of selling the whole produced electricity only on the day-ahead market. However, an increase of the profit is associated with a significant increase of the risk.