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Applied Mathematics Techniques for Energy Markets in Transition
Description and Aim
The world is witnessing a tremendous change in its energy supply mix, demand behavior
and market dynamics. Pivotal developments include ambitious climate change and environmental
policies, the progressive move to sustainable energy, the (at times sudden)
abandonment of polluting electricity generation, the growing availability of liquefied natural
gas and shale oil and gas. This all has a significant impact on the core business and
risk exposures of energy companies, on commodity and energy prices, and also on the
many financial energy derivative products traded. Changes in market mechanisms and
products demand novel mathematical models, stochastic and deterministic, microscopic
and macroscopic models, and changing pricing techniques, defining new research areas
within the field of applied mathematics.
Energy markets present unique challenges given very specific, inherent features, like
(practical) non-storability of electricity, seasonality trends and dramatic price spikes,
complex (often embedded) financial derivative structures, and strong dependence on
fundamental factors or political decision making. Furthermore, seasonal patterns exist
in demand and across various exogenous and endogenous fundamental price drivers, e.g.,
fuel prices, emission prices, weather conditions, market coupling mechanisms. Finally,
there are often strong regulations or subsidies by governmental authorities, driven by
energy and climate control policies. All of these require specially tailored mathematical
modelling and methods adapted to energy market applications, e.g., forward backward
stochastic differential equations (FBSDEs), Monte Carlo (MC) methods, nonlinear partial
(integro) differential equations (PDEs, PIDES), high-dimensionality, sparse grids,
recombination techniques, agent-based models and mean field game models.
In this workshop we wish to focus on three relevant, contemporary mathematical themes
to cover the different aspects. We envision ample, lively discussions between experts in
the fields of applied mathematics, computer science (heuristic algorithms, big data and
machine learning), as well as economics (the impact of a major transition). This makes
our foreseen workshop highly interactive and a stimulating, challenging experience.
(A) Risk management issues related to the energy transition
The goal of risk management is to assess quantitatively the likeliness of rare events as
well as their impact. With a major energy transition, there are by definition significant
risks that should be estimated and approximated by means of advanced, probabilistic and
numerical mathematics techniques. It is the tails of governing probability distributions
that need to be accurately determined and quantified. As the energy supply chain is
also politically impacted, it is important to quantitatively model impact of regulatory
demands regarding energy trading in the context of risk management.
In recent years, emerging renewable energy production, changes in power production due
to environmental policies, shifting commodity prices, domestic micro-generation and ageing
power grids, have fundamentally changed the future economic and political landscape
for energy providers and regulators in the European energy markets. Within this changing
environment, the ability to meet variable patterns of the aggregate energy demand
of a large number of households in Europe poses a huge challenge. So-called mean field
games models for the household energy demand, based on a stochastic demand process
for each household can be defined for the aggregate demand; inverse problems (optimized
cost-reward) can be studied like setting incentives (market price, demand-side management)
to balance load on the power grid and adjust demand to the variable production
(e.g., from renewable energy sources).
A variety of methods and ideas have been tried to forecast electricity loads and prices.
Engineers are aware that high-quality probabilistic price forecasts would help utilities
and independent power producers to submit effective bids, hence, help manage trading
portfolios and improve risk management practices. The increasing popularity of probabilistic
forecasts has, however, not been observed so far in electricity market research.
(B) Energy derivatives facilitating the energy transition
It may not be commonly known, but revenues of power plants are nowadays secured by
so-called financial energy derivatives. By means of these derivatives, the profit and losses
of power plants can be hedged against uncertain price fluctuations in for example gas or
electricity prices. They can play a prominent role in risk minimization.
Wind, solar and other forms of renewable energy are expected to take over a significant
part of the generation of power in the near future. Derivatives that are based on the
wind or solar intensity on specific local places on or off-shore are not yet traded, and the
need to hedge the case of "no-wind" or "no sun" is at present not yet urgent. However,
it is expected that these issues will become prominent in the mid-term future. Typical
energy products in this class of sustainable energy may be the so-called power swaps,
by which a "floating" (highly uncertain) source of power can be swapped for a more
steady source of power on a power exchange. Subsequent important energy derivatives
are spread options, such as the so-called clean spark spread options that secure revenues
made by a utility from selling power, having bought gas and other commodities, as well as
carbon allowances. Uncertain factors (electricity price, gas price, and cost of carbon) are
modeled by means of stochastic processes, so that multi-dimensional partial differential
equations result to value this kind of options. The aspect of high-dimensionality of the
governing equations deserves a special focus within our workshop.
Energy derivatives can vary in contract complexity and are highly interesting from a
numerical mathematics point of view. For example, the holder of a swing option can
often exercise at any time before maturity, subject to a penalty time based on the previous
exercise moments and/or amounts. Mathematical models are then based on control
problems with partial differential equations that need to be solved in a robust and efficient way.
Hamilton-Jacobi-Bellman equations are at the heart of the valuation of these contracts.
In this workshop we shall deal with the definition of modern energy derivative
contracts, their modelling as well as the numerical techniques to price these.
(C) Decisions for demand flexibilization in energy intensive industry
Industrial companies often have very high electricity demand as well as high potentials
to shift loads and to adapt to changes in market signals. However, exploitation
of these options needs a much deeper understanding of the technical potentials available,
e.g. consequences of investment decisions in innovative technology as well as the
rationalities governing investment decisions but also the changes in production and other
organizational processes in companies implied by a more responsive role with regards to
fluctuating electricity supply.
The objectives are better understanding, conceptualizing and modelling of (investment)
decisions in industrial companies regarding the interaction with the electricity market
(these include technical as well as operational characteristics and costs of flexibilization
of electricity demand and the related monetary as well as non-monetary influencing
factors) in depths study of inter-dependencies between companies (investment) decisions,
changes in electricity markets and organizational consequences within industrial sites
issues (in close collaboration with industrial stakeholders). Agent based models of the
investment and related decisions in industrial companies regarding a stronger interaction
of electricity demand with supply and respective price signals have been developed, and
in this workshop we aim to exchange the latest results. In-depth studies of the relevant
factors for investment decisions in industry following the example of one or more selected
branches (literature and intensive involvement with the industrial stakeholder network).
In a global and regulated market like the energy market, an important question is to
investigate the optimal portfolio of energy generation resources for a power utility. What
is the optimal portion for a utility of renewable (wind, sun) power, gas, coal and other
power plants? To which extent is a portfolio static (the base load) and how can we
make parts of it dynamically varying? Since Markowitz's pioneering work on a single-period
investment model, the mean-variance portfolio optimization problem has become
a cornerstone of investment management. Efficient algorithms for portfolio optimization
under constraints can be applied to energy markets. In particular, it appears necessary
to take liquidity constraints into account in the optimization. For utilities having a gas
portfolio in a less liquid market, the question is how to optimally make use of gas storage,
forward and spot trading (in their own market but also in more liquid markets), transport
(with more liquid markets) and swing option contracts? Clever algorithms have to be fed
by clever data. A related interesting question is whether so-called big data information
by means of deep learning and neural networks can become a useful asset in this context.