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Well-posedness and invariant measures for HJM models with deterministic volatility and Levy noise

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  • Carlo Marinelli

Abstract

We give sufficient conditions for the existence, uniqueness and ergodicity of invariant measures for Musiela's stochastic partial differential equation with deterministic volatility and a Hilbert space valued driving Levy noise. Conditions for the absence of arbitrage and for the existence of mild solutions are also discussed.

Suggested Citation

  • Carlo Marinelli, 2010. "Well-posedness and invariant measures for HJM models with deterministic volatility and Levy noise," Quantitative Finance, Taylor & Francis Journals, vol. 10(1), pages 39-47.
    • Handle: RePEc:taf:quantf:v:10:y:2010:i:1:p:39-47
    DOI: 10.1080/14697680802595692
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    Citations

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    Cited by:

    1. 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.
    2. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.
    3. Dennis Schroers, 2024. "Robust Functional Data Analysis for Stochastic Evolution Equations in Infinite Dimensions," Papers 2401.16286, arXiv.org, revised Jun 2024.
    4. Dennis Schroers, 2024. "Dynamically Consistent Analysis of Realized Covariations in Term Structure Models," Papers 2406.19412, arXiv.org.

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