The last decades have seen an expanding competition and complexity in the emerging
energy markets, mainly due to the increasing deregulation and privatization of
these markets. As a consequence, the dynamics of energy prices have become highly
volatile and so energy traders are calling for new instruments and techniques in order
to protect their exposures against the risks entailed by the energy markets. A key
issue in the energy markets is the fact that energy (in particular oil and gas) can be
stored physically. Such storage facilities allow for anticipating and exploiting market
fluctuations of energy prices according to the principle “sell high” and “buy low”.
Initially, storage facilities were only accessible by major players in the respective industries,
who had sufficient capital to build and maintain them. Meanwhile, due to
the emerging liberalization of the energy markets all participants have the possibility
to trade storage services via storage exchange platforms. As a consequence on the one
hand, design of optimal strategies involving buying, storing, and selling energy over
time are called for. On the other hand, this resulted in a high demand of proper statistical
prediction algorithms based on adequate statistical modeling of energy prices
and storage markets. This whole development has further led to the appearance of
structured contracts, also called energy derivatives. In the gas and energy markets
for example, so called “swing options” have become very popular. An example swing
option gives the holder the right to buy or sell a certain amount of gas, electricity or
storage capacity at a certain prescribed number of trading dates. Energy derivatives
are typically difficult to treat from a quantitative point of view due to their complex
structured exercise features and their highly pathdependent structure. As a general
consequence, the rising complexity of the markets poses a bunch of challenging
mathematical issues that are to be resolved. These issues may be categorized into the
following main streams:
 New numerical methods and algorithms for solving multidimensional problems in
optimal (multiple) stopping and optimal control
 Adequate modeling of various energy price processes including modern statistical
forecast techniques
Particularly in electricity markets, the evaluation of (swing) options requires efficient
algorithms for multiple stopping and more complicated control optimization problems.
Initially, the dual martingale approach was extended to general optimal control
problems by [BSS10]. A first breakthrough was achieved in [Sch12] where a new dual
martingale representation for multiple stopping problems was developed. This representation
has been extended to much more general payoff profiles in [BSZ15] (see also
[BMS13]). In this extended setting it is possible to treat more realistic energy derivatives
by the Monte Carlo method. Such derivatives may involve several volume and
exercise refraction constraints, as well as processes driving several underlying energy
titles. A novel simulation based primal approach for (standard) multiple stopping,
hence the pricing of (simply structured) swing options was developed in [BS06]. A
main general goal is the highly nontrivial extension of the above mentioned methods
to problems of general control optimization.
