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Affine realizations with affine state processes for stochastic partial differential equations

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  • Tappe, Stefan

Abstract

The goal of this paper is to clarify when a stochastic partial differential equation with an affine realization admits affine state processes. This includes a characterization of the set of initial points of the realization. Several examples, as the HJMM equation from mathematical finance, illustrate our results.

Suggested Citation

  • Tappe, Stefan, 2016. "Affine realizations with affine state processes for stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 126(7), pages 2062-2091.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:7:p:2062-2091
    DOI: 10.1016/j.spa.2016.01.004
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    References listed on IDEAS

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    1. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2016. "A general HJM framework for multiple yield curve modelling," Finance and Stochastics, Springer, vol. 20(2), pages 267-320, April.
    2. Tomas Björk & Lars Svensson, 2001. "On the Existence of Finite‐Dimensional Realizations for Nonlinear Forward Rate Models," Mathematical Finance, Wiley Blackwell, vol. 11(2), pages 205-243, April.
    3. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    4. Darrell Duffie & Rui Kan, 1996. "A Yield‐Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406, October.
    5. Francesca Biagini & Alessandro Gnoatto & Maximilian Hartel, 2013. "Affine HJM Framework on $S_{d}^{+}$ and Long-Term Yield," Papers 1311.0688, arXiv.org, revised Aug 2015.
    6. Eckhard Platen & Steffan Tappe, 2015. "Real-World Forward Rate Dynamics With Affine Realizations," Published Paper Series 2015-7, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    7. Alan Brace & Marek Musiela, 1994. "A Multifactor Gauss Markov Implementation Of Heath, Jarrow, And Morton," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 259-283, July.
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    Cited by:

    1. Schmidt, Thorsten & Tappe, Stefan & Yu, Weijun, 2020. "Infinite dimensional affine processes," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7131-7169.

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