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Polynomial processes have the property that expectations of polynomial functions (of degree $n$, say) of the future state of the process conditional on the current state are given by polynomials (of degree $\leq n$) of the current state.…
We develop efficient methods for simulating processes of Ornstein-Uhlenbeck type related to the class of $p$-tempered $\alpha$-stable ($\ts$) distributions. Our results hold for both the univariate and multivariate cases and we consider…
This paper considers the representation of energy storage in electricity sector capacity planning models. The incorporation of storage in long-term systems models of this type is increasingly relevant as the cost of storage technologies,…
The Ornstein-Uhlenbeck (OU) process, a mean-reverting stochastic process, has been widely applied as a time series model in various domains. This paper describes the design and implementation of a model-based synthetic time series model…
We study the $G/\mathit{GI}/\infty$ queue in heavy-traffic using tempered distribution-valued processes which track the age and residual service time of each customer in the system. In both cases, we use the continuous mapping theorem…
We conduct a preliminary analysis of a pairs trading strategy using the Ornstein-Uhlenbeck (OU) process to model stock price spreads. We compare this approach to a naive pairs trading strategy that uses a rolling window to calculate mean…
This paper proposes an agent-based model that combines both spot and balancing electricity markets. From this model, we develop a multi-agent simulation to study the integration of the consumers' flexibility into the system. Our study…
This paper develops power series expansions of a general class of moment functions, including transition densities and option prices, of continuous-time Markov processes, including jump--diffusions. The proposed expansions extend the ones…
Intraday electricity markets play an increasingly important role in balancing the intermittent generation of renewable energy resources, which creates a need for accurate probabilistic price forecasts. However, research to date has focused…
Modern market management systems continue to evolve due to the intentions to improve system security and reliability. This evolvement has been leading to a transition of market auction models from a deterministic structure with…
We examine the novel problem of the estimation of transaction arrival processes in the intraday electricity markets. We model the inter-arrivals using multiple time-varying parametric densities based on the generalized F distribution…
We propose a parsimonious stochastic model for characterising the distributional and temporal properties of rainfall. The model is based on an integrated Ornstein-Uhlenbeck process driven by the Hougaard L\'evy process. We derive properties…
Accurate and reliable electricity price forecasting has significant practical implications for grid management, renewable energy integration, power system planning, and price volatility management. This study focuses on enhancing…
A minimal model of a market of myopic non-cooperative agents who trade bilaterally with random bids reproduces qualitative features of short-term electric power markets, such as those in California and New England. Each agent knows its own…
In electricity markets, it is sensible to use a two-factor model with mean reversion for spot prices. One of the factors is an Ornstein-Uhlenbeck (OU) process driven by a Brownian motion and accounts for the small variations. The other…
Functional data present as functions or curves possessing a spatial or temporal component. These components by nature have a fixed observational domain. Consequently, any asymptotic investigation requires modelling the increased correlation…
We use simulation to compare different power flow models in the process of charging electric vehicles (EVs) by considering their random arrivals, their stochastic demand for energy at charging stations, and the characteristics of the…
The shortcomings of the popular Black-Scholes-Merton (BSM) model have led to models which could more accurately model the behavior of the underlying assets in energy markets, particularly in electricity and future oil prices. In this paper…
The problem of heat and electricity pricing in combined heat and power systems regarding the time scales of electricity and heat, as well as thermal energy quality, is studied. Based on the asynchronous coordinated dispatch of the combined…
Electricity is traded on various markets with different time horizons and regulations. Short-term intraday trading becomes increasingly important due to the higher penetration of renewables. In Germany, the intraday electricity price…