nach oben

Erschienen in:

2023 | OriginalPaper | Buchkapitel

2. Lévy processes on Hilbert Spaces

verfasst von : Fred Espen Benth, Paul Krühner

Erschienen in: Stochastic Models for Prices Dynamics in Energy and Commodity Markets

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

We introduce and study Lévy process in Hilbert space. These processes are the basic noise drivers in the forward price dynamics. Explicit constructions based on subordination of Wiener process to define normal inverse Gaussian, stable and variance-gamma Lévy processes with values in Hilbert space are provided.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Vorheriges Kapitel Introduction

Nächstes Kapitel The Filipović Space and Operators

the French acronym càdlàg means continuous from the right, limits from the left.

By \(\boldsymbol {\theta }\leq \boldsymbol {\theta }_1\) we mean that \(\theta _j\leq \theta _{1,j}\) for all \(j=1,\ldots ,d\).

Albert, A. (1972). Regression and the Moore-Penrose Pseudoinverse. Academic Press, New York.MATH

Andersen, A., Koekebakker, S., and Westgaard, S. (2010). Modeling electricity forward prices using the multivariate normal inverse Gaussian distribution. Journal of Energy Markets, 3(3), pp. 3–25.CrossRef

Ané, T., and Geman, H. (2000). Order flow, transaction clock, and normality of asset returns. Journal of Finance, 55(5), pp. 2259–2284.CrossRef

10.

Baeumer, B., Kovács, M., and Meerschaert, M. M. (2008). Subordinated multiparameter groups of linear operators: Properties via the transference principle. In Functional Analysis and Evolution Equations. The Günter Lumer Volume, Amann, H., Arendt, W., Hieber, M., Neubrander, F., Nicaise, S. and J. von Below (eds.), Birkhäuser Verlag, Basel Boston Berlin, pp. 35–50.

11.

Barndorff-Nielsen, O. E. (1977). Exponentially decreasing distributions for the logarithm of particle size. Proceedings of the Royal Society of London, Series A, 353(1674), pp. 401–409.

14.

Barndorff-Nielsen, O. E., Benth, F. E., and Veraart, A. (2014). Modelling electricity futures by ambit fields. Advances in Applied Probability, 46(3), pp. 719–745.MathSciNetCrossRefMATH

16.

Barndorff-Nielsen, O. E., Pedersen, J., and Sato, K. (2001). Multivariate subordination, self-decomposability and stability. Advances in Applied Probability, 33(1), pp. 160–187.MathSciNetCrossRefMATH

17.

Barndorff-Nielsen, O. E., and Schmiegel, J. (2004), Lévy-based tempo-spatial modelling with applications to turbulence. Uspekhi Mat. NAUK, 59, pp. 65–91.MATH

31.

Benth, F. E., Klüppelberg, C., Müller, G., and Vos, L. (2014). Futures pricing in electricity markets based on stable CARMA spot models. Energy Economics, 44, pp. 392–406.CrossRef

35.

Benth, F. E., and Krühner, P. (2015) Subordination of Hilbert space valued Lévy processes. Stochastics, 87(3), pp. 458–476.MathSciNetCrossRefMATH

37.

Benth, F. E., and Krühner, P. (2015). Derivatives pricing in energy markets: an infinite dimensional approach. SIAM Journal of Financial Mathematics, 6(1), pp. 825–869.MathSciNetCrossRefMATH

48.

Benth, F. E., and Šaltytė Benth (2012). Stochastic modelling of temperature variations with a view towards weather derivatives. Applied Mathematical Finance, 12(1), pp. 53–85.CrossRefMATH

49.

Benth, F. E., and Šaltytė Benth (2012). Modelling and Pricing in Financial Markets for Weather Derivatives. World Scientific, Singapore.CrossRefMATH

56.

Bertoin, J. (1996). Lévy Processes. Cambridge University Press, Cambridge.MATH

61.

Bochner, S. (1949). Diffusion equation and stochastic processes. Proceedings of the National Academy of Sciences of the United States of America, 35, (7), pp. 368–370.MathSciNetCrossRefMATH

63.

Borovkova, S., and Schmeck, M. D. (2017). Electricity price modeling with stochastic time change. Energy Economics, 63, pp. 51–65.CrossRef

69.

Carmona, R., and Teranchi, M. (2006). Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective. Springer-Verlag, Berlin Heidelberg New York.

73.

Conway, J. (1990). A Course in Functional Analysis, 2nd Ed., Springer-Verlag, New York.MATH

90.

Eberlein, E., Jacod, J., and Raible, S. (2005). Lévy term structure models: No-arbitrage and completeness. Finance & Stochastics, 9, pp. 67–88.MathSciNetCrossRefMATH

91.

Eberlein, E., and Keller, U. (1995). Hyperbolic distributions in finance. Bernoulli, 1, pp. 281–299.CrossRefMATH

92.

Eberlein, E., and Stahl, G. (2003). Both sides of the fence: A statistical and regulatory view of electricity risk. Energy Risk, 8, pp. 34–38.

96.

Ethier, S. and Kurtz, T. (1986). Markov Processes. Characterization and Convergence. John Wiley & Sons, New York.CrossRefMATH

107.

Frestad, D., Benth, F. E., and Koekebakker, S. (2010). Modeling term structure dynamics in the Nordic electricity swap market. Energy Journal, 31(2), pp. 53–86.CrossRef

109.

Garcia, I., Klüppelberg, C., and Müller, G. (2011). Estimation of stable carma models with an application to electricity spot prices. Statistical Modelling, 11, pp. 447 470.

112.

Geman, H., Madan, D. B., and Yor, M. (2001). Time changes for Lévy processes. Mathematical Finance, 11(1), pp. 79–96.MathSciNetCrossRefMATH

118.

Goutte, S., Oudjane, N., and Russo, F. (2014). Variance optimal hedging for continuous time additive processes and applications. Stochastics, 86, pp. 147–185.MathSciNetCrossRefMATH

124.

Hinderks, W. J., and Wagner, A. (2020). Factor models in the German electricity market: Stylized facts, seasonality, and calibration. Energy Economics, 85, article 104351.

142.

Kremer, M., Benth, F. E., Felten, B., and Kiesel, R. (2020). Volatility and liqudity on high-frequency electricity futures markets: empirical analysis and stochastic modeling. International Journal of Theoretical and Applied Finance, 23(4), pp. 1–38.CrossRefMATH

145.

Ladokhin, S., Schmeck, M. D., and Borovkova, S. (2021). Commodity forward curves with stochastic time change. E-print July, available on ssrn: 3871680.

148.

Linde, W. (1983). Infinitely Divisible and Stable Measures on Banach Spaces.. B. G. Teubner Verlagsgesellschaft, Leipzig.

151.

Madan, D., Carr, P., and Chang, E. (1998). The variance gamma process and option pricing. European Finance Review, 2, pp. 79–105.CrossRefMATH

152.

Madan, D., and Seneta, E. (1990). The VG model for share market returns. Journal of Business, 63(4), pp. 511–524.CrossRef

156.

Mendoza-Arriaga, R., and Linetsky, V. (2016). Multivariate subordination of Markov processes with financial applications. Mathematical Finance, 26(4), pp. 699–747.MathSciNetCrossRefMATH

160.

Øigård, T. A., and Hanssen, A. (2002). The multivariate normal inverse Gaussian heavy-tailed distribution: simulation and estimation. In 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Vol. 2, pp. II–1489 - II–1492.

162.

Parthasarathy, K. R. (1967). Probability Measures on Metric Spaces. Academic Press, New York-London.CrossRefMATH

163.

Pedersen, G. K. (1989). Analysis Now, Springer-Verlag, New York,CrossRefMATH

164.

Pérez-Abreu, V., and Rocha-Arteaga, A. (2005). Covariance-parameter Lévy processes in the space of trace-class operators. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 8(1), pp. 33–54.MathSciNetCrossRefMATH

165.

Peszat, S., and Zabczyk, J. (2007). Stochastic Partial Differential Equations with Lévy Noise. Cambridge University Press, Cambridge.CrossRefMATH

166.

Piccirilli, M., Schmeck, M. D:, and Vargiolu, T. (2021). Capturing the power options smile by an additive two-factor model for overlapping futures prices. Energy Economics, 95, article 105006.

172.

Rydberg, T. (1997). The normal inverse Gaussian Lévy process: simulation and approximation. Communications in Statistics. Stochastic Models, 13, pp. 887–910.MathSciNetCrossRefMATH

175.

Sato, K. (1999). Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press, Cambridge.MATH

179.

Skorohod, A. V. (1991). Random Processes with Independent Increments. Kluwer Academic Press, Mathematics and its Applications Vol. 47.

Titel: Lévy processes on Hilbert Spaces
verfasst von: Fred Espen Benth
Paul Krühner
Verlag: Springer International Publishing
Buch: Stochastic Models for Prices Dynamics in Energy and Commodity Markets
Print ISBN: 978-3-031-40366-8

Electronic ISBN: 978-3-031-40367-5

Copyright-Jahr: 2023
DOI: https://doi.org/10.1007/978-3-031-40367-5_2