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## Applied Mathematics Techniques for Energy Markets in Transition |

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.
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.
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.
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. [Back] |