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Aims. Numerical test-particle simulations are a reliable and frequently used tool to test analytical transport theories and to predict mean-free paths. The comparison between solutions of the diffusion equation and the particle flux is used…
The increasing interest in demand-side management (DSM) as part of the energy cost optimization calls for effective methods to determine representative electricity prices for energy optimization and scheduling investigations. We propose a…
In this paper we analyze a nonlinear Black--Scholes model for option pricing under variable transaction costs. The diffusion coefficient of the nonlinear parabolic equation for the price $V$ is assumed to be a function of the underlying…
Intra-day price spreads are of interest to electricity traders, storage and electric vehicle operators. This paper formulates dynamic density functions, based upon skewed-t and similar representations, to model and forecast the German…
This article investigates the Fokker-Planck equations that arise from the application of quantum stochastic calculus to the modelling of illiquid financial markets, using asymptotic methods. We present a power series solution for quantum…
This paper proposes a novel purely measurement-based method for estimating dynamic load parameters in near real-time when stochastic load fluctuations are present. By leveraging on the regression theorem for the Ornstein-Uhlenbeck process,…
This paper introduces a novel Bayesian reverse unrestricted mixed-frequency model applied to a panel of nine European electricity markets. Our model analyzes the impact of daily fossil fuel prices and hourly renewable energy generation on…
In this paper, a purely measurement-based method is proposed to estimate the dynamic system state matrix by applying the regression theorem of the multivariate Ornstein-Uhlenbeck process. The proposed method employs a recursive algorithm to…
We study the positive recurrence of piecewise Ornstein-Uhlenbeck (OU) diffusion processes, which arise from many-server queueing systems with phase-type service requirements. These diffusion processes exhibit different behavior in two…
In this paper, we focus on option pricing models based on space-time fractional diffusion. We briefly revise recent results which show that the option price can be represented in the terms of rapidly converging double-series and apply these…
Electrical load forecasting plays a crucial role in decision-making for power systems, including unit commitment and economic dispatch. The integration of renewable energy sources and the occurrence of external events, such as the COVID-19…
In an electric power system, demand fluctuations may result in significant ancillary cost to suppliers. Furthermore, in the near future, deep penetration of volatile renewable electricity generation is expected to exacerbate the variability…
The problem of heat system pricing is considered. A direct extension of locational marginal prices (LMP) in electricity markets to heat systems may lead to revenue inadequate issues. The underlying reason for such a problem is that, unlike…
Data centers (DCs) are emerging as large, geographically distributed, controllable loads whose participation in electricity markets can significantly affect grid operation, especially when cloud platforms shift workloads across sites to…
In this paper hyperbolic partial differential equations with random coefficients are discussed. Such random partial differential equations appear for instance in traffic flow problems as well as in many physical processes in random media.…
Two main approaches in particle-based simulations for modeling a charged surface are using explicit, discrete charges and continuum, uniform charges. It is well-known that these two approaches could lead to substantially distinct ionic…
We consider the problem of option pricing under stochastic volatility models, focusing on the linear approximation of the two processes known as exponential Ornstein-Uhlenbeck and Stein-Stein. Indeed, we show they admit the same limit…
Accurate electrical load forecasting is crucial for optimizing power system operations, planning, and management. As power systems become increasingly complex, traditional forecasting methods may fail to capture the intricate patterns and…
Since the 1990s, widespread introduction of central (wholesale) electricity markets has been seen across multiple continents, driven by the search for efficient operation of the power grid through competition. The increase of renewables has…
The growing adoption of electric vehicles (EVs) is increasing peak demand in distribution systems, which can threaten grid stability and reduce operational efficiency. Dynamic electricity pricing is a promising means of mitigating these…