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The forward dynamics in energy markets - infinite dimensional modeling and simulation

Barth, Andrea; Benth, Fred Espen
Journal article; AcceptedVersion; Peer reviewed
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paper1.pdf (835.1Kb)
Year
2014
Permanent link
http://urn.nb.no/URN:NBN:no-46299

CRIStin
1178416

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Appears in the following Collection
  • Matematisk institutt [2452]
  • CRIStin høstingsarkiv [15935]
Original version
Stochastics: An International Journal of Probability and Stochastic Processes. 2014, 86 (6), 932-966, DOI: http://dx.doi.org/10.1080/17442508.2014.895359
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.
 
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