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Invariant measures for the Musiela equation with deterministic diffusion term

Author

Listed:
  • Tiziano Vargiolu

    (Dipartimento di Matematica Pura ed Applicata, Universit di Padova, via Belzoni 7, I-35131 Padova, Italy Manuscript)

Abstract

In this article the forward rates equation of the Musiela model is analysed. The equation is studied in the Sobolev spaces $H^1_\gamma({\Bbb R}^+)$ and $H^1({\Bbb R}^+)$. Explicit mild solutions and equivalent conditions for the existence and uniqueness of invariant measures are presented.

Suggested Citation

  • Tiziano Vargiolu, 1999. "Invariant measures for the Musiela equation with deterministic diffusion term," Finance and Stochastics, Springer, vol. 3(4), pages 483-492.
    • Handle: RePEc:spr:finsto:v:3:y:1999:i:4:p:483-492
    Note: received: June 1996; final revision received: November 1998
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    Citations

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    Cited by:

    1. Salvatore Federico, 2011. "A stochastic control problem with delay arising in a pension fund model," Finance and Stochastics, Springer, vol. 15(3), pages 421-459, September.
    2. Marek Musiela, 2022. "My journey through finance and stochastics," Finance and Stochastics, Springer, vol. 26(1), pages 33-58, January.
    3. Zdzisław Brzeźniak & Tayfun Kok, 2018. "Stochastic evolution equations in Banach spaces and applications to the Heath–Jarrow–Morton–Musiela equations," Finance and Stochastics, Springer, vol. 22(4), pages 959-1006, October.
    4. Zdzislaw Brzezniak & Tayfun Kok, 2016. "Stochastic Evolution Equations in Banach Spaces and Applications to Heath-Jarrow-Morton-Musiela Equation," Papers 1608.05814, arXiv.org.
    5. Dennis Schroers, 2024. "Robust Functional Data Analysis for Stochastic Evolution Equations in Infinite Dimensions," Papers 2401.16286, arXiv.org.
    6. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    7. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.

    More about this item

    Keywords

    term structure of interest rates; stochastic partial differential equations; mild solutions; invariant measures; $C^0$-semigroups in Hilbert spaces;
    All these keywords.

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects

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