Abstract and Applied Analysis

Compact Embeddings for Spaces of Forward Rate Curves

Stefan Tappe

Full-text: Open access

Abstract

The goal of this paper is to prove a compact embedding result for spaces of forward rate curves. As a consequence of this result, we show that any forward rate evolution can be approximated by a sequence of finite dimensional processes in the larger state space.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 709505, 6 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393512073

Digital Object Identifier
doi:10.1155/2013/709505

Mathematical Reviews number (MathSciNet)
MR3111796

Zentralblatt MATH identifier
07095259

Citation

Tappe, Stefan. Compact Embeddings for Spaces of Forward Rate Curves. Abstr. Appl. Anal. 2013 (2013), Article ID 709505, 6 pages. doi:10.1155/2013/709505. https://projecteuclid.org/euclid.aaa/1393512073


Export citation

References

  • D. Filipović, Consistency Problems for Heath-Jarrow-Morton Interest Rate Models, vol. 1760 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 2001.
  • A. Rusinek, “Mean reversion for HJMM forward rate models,” Advances in Applied Probability, vol. 42, no. 2, pp. 371–391, 2010.
  • M. Barski and J. Zabczyk, “Heath-Jarrow-Morton-Musiela equation with Lévy perturbation,” Journal of Differential Equations, vol. 253, no. 9, pp. 2657–2697, 2012.
  • D. Filipović and S. Tappe, “Existence of Lévy term structure models,” Finance and Stochastics, vol. 12, no. 1, pp. 83–115, 2008.
  • D. Filipović, S. Tappe, and J. Teichmann, “Term structure models driven by Wiener processes and Poisson measures: existence and positivity,” SIAM Journal on Financial Mathematics, vol. 1, no. 1, pp. 523–554, 2010.
  • W. Rudin, Functional Analysis, International Series in Pure and Applied Mathematics, McGraw-Hill, New York, NY, USA, 2nd edition, 1991.
  • D. Werner, Funktionalanalysis, Springer, Berlin, Germany, 2007.
  • H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Universitext, Springer, New York, NY, USA, 2011.
  • R. A. Adams and J. J. F. Fournier, Sobolev Spaces, vol. 140 of Pure and Applied Mathematics, Elsevier/Academic Press, Amsterdam, The Netherlands, 2nd edition, 2003.
  • D. Filipović, S. Tappe, and J. Teichmann, “Jump-diffusions in Hilbert spaces: existence, stability and numerics,” Stochastics, vol. 82, no. 5, pp. 475–520, 2010.