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Invariant measures for the Musiela equation with deterministic diffusion term


  • Tiziano Vargiolu

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


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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    References listed on IDEAS

    1. Jaime Cuevas Dermody & R. Tyrrell Rockafellar, 1991. "Cash Stream Valuation In the Face of Transaction Costs and Taxes," Mathematical Finance, Wiley Blackwell, vol. 1(1), pages 31-54.
    2. Bernard Bensaid & Jean-Philippe Lesne & Henri Pagès & José Scheinkman, 1992. "Derivative Asset Pricing With Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 63-86.
    3. Lukasz Stettner, 2000. "Option Pricing in Discrete-Time Incomplete Market Models," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 305-321.
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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. Zdzislaw Brzezniak & Tayfun Kok, 2016. "Stochastic Evolution Equations in Banach Spaces and Applications to Heath-Jarrow-Morton-Musiela Equation," Papers 1608.05814,
    3. 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.
    4. 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


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

    JEL classification:

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


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