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.

Background

(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.