In this paper an infinite-dimensional approach to model energy forward markets is introduced. Similar to the Heath–Jarrow–Morton framework in interest-rate modelling, a first-order hyperbolic stochastic partial differential equation models the dynamics of the forward price curves. These equations are analysed, and in particular regularity and no-arbitrage conditions in the general situation of stochastic partial differential equations driven by an infinite-dimensional martingale process are studied. Both arithmetic and geometric forward price dynamics are studied, as well as accounting for the delivery period of electricity forward contracts. A stable and convergent numerical approximation in the form of a finite element method for hyperbolic stochastic partial differential equations is introduced and applied to some examples with relevance to energy markets.
%0 Journal Article
%1 barth2014forward
%A Barth, Andrea
%A Benth, Fred Espen
%D 2014
%J Stochastics
%K 2014 B07 sfbtrr161
%N 6
%P 932-966
%R 10.1080/17442508.2014.895359
%T The Forward Dynamics in Energy Markets - Infinite-dimensional Modelling and Simulation
%U http://dx.doi.org/10.1080/17442508.2014.895359
%V 86
%X In this paper an infinite-dimensional approach to model energy forward markets is introduced. Similar to the Heath–Jarrow–Morton framework in interest-rate modelling, a first-order hyperbolic stochastic partial differential equation models the dynamics of the forward price curves. These equations are analysed, and in particular regularity and no-arbitrage conditions in the general situation of stochastic partial differential equations driven by an infinite-dimensional martingale process are studied. Both arithmetic and geometric forward price dynamics are studied, as well as accounting for the delivery period of electricity forward contracts. A stable and convergent numerical approximation in the form of a finite element method for hyperbolic stochastic partial differential equations is introduced and applied to some examples with relevance to energy markets.
@article{barth2014forward,
abstract = {In this paper an infinite-dimensional approach to model energy forward markets is introduced. Similar to the Heath–Jarrow–Morton framework in interest-rate modelling, a first-order hyperbolic stochastic partial differential equation models the dynamics of the forward price curves. These equations are analysed, and in particular regularity and no-arbitrage conditions in the general situation of stochastic partial differential equations driven by an infinite-dimensional martingale process are studied. Both arithmetic and geometric forward price dynamics are studied, as well as accounting for the delivery period of electricity forward contracts. A stable and convergent numerical approximation in the form of a finite element method for hyperbolic stochastic partial differential equations is introduced and applied to some examples with relevance to energy markets.},
added-at = {2020-03-05T13:44:29.000+0100},
author = {Barth, Andrea and Benth, Fred Espen},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/21ccb8fa8f448c56611a5d79bb9e48d0e/leonkokkoliadis},
doi = {10.1080/17442508.2014.895359},
fjournal = {Stochastics. An International Journal of Probability and Stochastic
Processes},
interhash = {5393708753859534ac8e91543a966870},
intrahash = {1ccb8fa8f448c56611a5d79bb9e48d0e},
issn = {1744-2508},
journal = {Stochastics},
keywords = {2014 B07 sfbtrr161},
mrclass = {Preliminary Data},
mrnumber = {3271515},
number = 6,
owner = {seusdd},
pages = {932-966},
timestamp = {2020-03-05T12:44:29.000+0100},
title = {The Forward Dynamics in Energy Markets - Infinite-dimensional Modelling and Simulation},
url = {http://dx.doi.org/10.1080/17442508.2014.895359},
volume = 86,
year = 2014
}
