×

zbMATH — the first resource for mathematics

The forward dynamics in energy markets – infinite-dimensional modelling and simulation. (English) Zbl 1337.91086
Summary: 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.

MSC:
91G20 Derivative securities (option pricing, hedging, etc.)
91B74 Economic models of real-world systems (e.g., electricity markets, etc.)
60H30 Applications of stochastic analysis (to PDEs, etc.)
91G60 Numerical methods (including Monte Carlo methods)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Andresen A., J. Energ. Markets 3 (3) pp 3– (2010) · doi:10.21314/JEM.2010.051
[2] N.Audet, P.Heiskanen, J.Keppo, and I.Vehviläinen, Modeling electricity forward curve dynamics in the Nordic market, in Modeling Prices in Competitive Markets, John Wiley & Sons, Chichester, 2004, pp. 252–265.
[3] J. Adv. Appl. Probab (2014)
[4] Barth A., Commun. Stoch. Anal. 4 (3) pp 355– (2009)
[5] DOI: 10.1016/j.spa.2013.01.003 · Zbl 1263.60063 · doi:10.1016/j.spa.2013.01.003
[6] DOI: 10.1007/s00245-012-9176-y · Zbl 1260.60134 · doi:10.1007/s00245-012-9176-y
[7] DOI: 10.1080/00207160.2012.701735 · Zbl 1270.65003 · doi:10.1080/00207160.2012.701735
[8] Barth A., Stochastics 84 pp 217– (2012)
[9] DOI: 10.1007/978-3-319-00413-6_2 · Zbl 1315.91022 · doi:10.1007/978-3-319-00413-6_2
[10] DOI: 10.1016/j.jbankfin.2007.12.022 · doi:10.1016/j.jbankfin.2007.12.022
[11] DOI: 10.1080/13504860600725031 · Zbl 1160.91337 · doi:10.1080/13504860600725031
[12] DOI: 10.1016/j.eneco.2007.06.005 · doi:10.1016/j.eneco.2007.06.005
[13] DOI: 10.3905/jod.2007.694791 · doi:10.3905/jod.2007.694791
[14] Benth F.E., J. Energ. Markets 2 (3) pp 111– (2009) · doi:10.21314/JEM.2009.021
[15] F.E.Benth, J.Saltyte Benth, and S.Koekebakker, Stochastic Modeling of Electricity and Related Markets, World Scientific, Singapore, 2008. · Zbl 1143.91002 · doi:10.1142/6811
[16] Bernhardt C., J. Energ. Markets 1 (1) pp 3– (2008) · doi:10.21314/JEM.2008.002
[17] DOI: 10.1007/978-3-642-12067-1_11 · doi:10.1007/978-3-642-12067-1_11
[18] DOI: 10.1007/s007800050069 · Zbl 0947.60051 · doi:10.1007/s007800050069
[19] Carmona R., Springer Finance (2006)
[20] Chow P.-L., Chapman & Hall/CRC, Applied Mathematics and Nonlinear Science Series (2007)
[21] DOI: 10.1017/CBO9780511666223 · doi:10.1017/CBO9780511666223
[22] DOI: 10.1007/BF01450498 · Zbl 0865.90014 · doi:10.1007/BF01450498
[23] DOI: 10.1137/0711052 · Zbl 0293.65077 · doi:10.1137/0711052
[25] DOI: 10.1214/105051605000000160 · Zbl 1125.91051 · doi:10.1214/105051605000000160
[26] Filipović D., Lecture Notes in Mathematics (2001)
[27] Filipović D., Stochastics 82 (5) pp 475– (2010)
[28] DOI: 10.1016/j.eneco.2006.12.001 · doi:10.1016/j.eneco.2006.12.001
[29] DOI: 10.5547/ISSN0195-6574-EJ-Vol31-No2-3 · doi:10.5547/ISSN0195-6574-EJ-Vol31-No2-3
[30] Geman H., Wiley-Finance (2005)
[31] DOI: 10.2307/2951677 · Zbl 0751.90009 · doi:10.2307/2951677
[32] DOI: 10.1137/09077271X · Zbl 1198.91230 · doi:10.1137/09077271X
[33] DOI: 10.1007/978-0-387-72067-8 · doi:10.1007/978-0-387-72067-8
[34] Koekebakker S., Manage. Financ. 31 (6) pp 74– (2005)
[35] Larsson S., Texts in Applied Mathematics (2003)
[36] DOI: 10.1111/j.1467-9965.2010.00403.x · Zbl 1193.91188 · doi:10.1111/j.1467-9965.2010.00403.x
[37] DOI: 10.1017/CBO9780511721373 · Zbl 1205.60122 · doi:10.1017/CBO9780511721373
[38] C.Prévôt and M.Röckner, A Concise Course on Stochastic Partial Differential Equations, Springer, Berlin, Heidelberg, New York, 2007. · Zbl 1123.60001
[39] DOI: 10.1007/978-3-662-10061-5 · doi:10.1007/978-3-662-10061-5
[40] A.M.Quarteroni and A.Valli, Numerical Approximation of Partial Differential Equations, Springer, Berlin, Heidelberg, New York, 2008. · Zbl 1151.65339
[41] DOI: 10.1080/15326349708807456 · Zbl 0899.60036 · doi:10.1080/15326349708807456
[42] DOI: 10.1142/9789812385192 · doi:10.1142/9789812385192
[43] DOI: 10.1002/0470870230 · doi:10.1002/0470870230
[44] DOI: 10.1111/j.1540-6261.1997.tb02721.x · doi:10.1111/j.1540-6261.1997.tb02721.x
[45] R.Wait and A.R.Mitchell, Finite Element Analysis and Applications, Wiley, Chichester, 1985. · Zbl 0577.65093
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.