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A note on invariant measures for HJM models

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  • Michael Tehranchi

Abstract

This note analyzes the mean-reverting behavior of time-homogeneous Heath-Jarrow-Morton (HJM) forward rate models in the weighted Sobolev spaces {H w } w . An explicit sufficient condition is given under which invariant measures exist for the HJM dynamics. In particular, every HJM model with constant volatility and market price of risk has a family of invariant measures parametrized by the distribution of the long rate. Copyright Springer-Verlag Berlin/Heidelberg 2005

Suggested Citation

  • Michael Tehranchi, 2005. "A note on invariant measures for HJM models," Finance and Stochastics, Springer, vol. 9(3), pages 389-398, July.
    • Handle: RePEc:spr:finsto:v:9:y:2005:i:3:p:389-398
    DOI: 10.1007/s00780-004-0143-6
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    Citations

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    Cited by:

    1. Damir Filipović & Stefan Tappe, 2008. "Existence of Lévy term structure models," Finance and Stochastics, Springer, vol. 12(1), pages 83-115, January.
    2. David Criens, 2018. "Deterministic Criteria For The Absence And Existence Of Arbitrage In Multi-Dimensional Diffusion Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-41, February.
    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. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.
    5. Toshiyuki Nakayama & Stefan Tappe, 2022. "Distance between closed sets and the solutions to stochastic partial differential equations," Papers 2205.00279, arXiv.org.
    6. Dennis Schroers, 2024. "Robust Functional Data Analysis for Stochastic Evolution Equations in Infinite Dimensions," Papers 2401.16286, arXiv.org.
    7. Damir Filipovi'c & Stefan Tappe, 2019. "Existence of L\'evy term structure models," Papers 1907.03561, arXiv.org.

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