{"title":"The forward dynamics in energy markets – infinite-dimensional modelling and simulation","authors":"A. Barth, F. Benth","doi":"10.1080/17442508.2014.895359","DOIUrl":null,"url":null,"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.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"18","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/17442508.2014.895359","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 18
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.