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Affine pure-jump processes on positive Hilbert–Schmidt operators

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  • Cox, Sonja
  • Karbach, Sven
  • Khedher, Asma

Abstract

We show the existence of a broad class of affine Markov processes on the cone of positive self-adjoint Hilbert–Schmidt operators. Such processes are well-suited as infinite-dimensional stochastic covariance models. The class of processes we consider is an infinite-dimensional analogue of the affine processes on the cone of positive semi-definite and symmetric matrices studied in Cuchiero et al. (2011).

Suggested Citation

  • Cox, Sonja & Karbach, Sven & Khedher, Asma, 2022. "Affine pure-jump processes on positive Hilbert–Schmidt operators," Stochastic Processes and their Applications, Elsevier, vol. 151(C), pages 191-229.
    • Handle: RePEc:eee:spapps:v:151:y:2022:i:c:p:191-229
    DOI: 10.1016/j.spa.2022.05.008
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    References listed on IDEAS

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    1. Christa Cuchiero & Josef Teichmann, 2011. "Path properties and regularity of affine processes on general state spaces," Papers 1107.1607, arXiv.org, revised Jan 2013.
    2. Schmidt, Thorsten & Tappe, Stefan & Yu, Weijun, 2020. "Infinite dimensional affine processes," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7131-7169.
    3. Christa Cuchiero & Damir Filipovi'c & Eberhard Mayerhofer & Josef Teichmann, 2009. "Affine processes on positive semidefinite matrices," Papers 0910.0137, arXiv.org, revised Apr 2011.
    4. Philipp Doersek & Josef Teichmann, 2010. "A Semigroup Point Of View On Splitting Schemes For Stochastic (Partial) Differential Equations," Papers 1011.2651, arXiv.org.
    5. Peter Spreij & Enno Veerman & Peter Vlaar, 2011. "An Affine Two-Factor Heteroskedastic Macro-Finance Term Structure Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(4), pages 331-352.
    6. Fred Espen Benth & Paul Kruhner, 2014. "Representation of infinite dimensional forward price models in commodity markets," Papers 1403.4111, arXiv.org.
    7. Benth, Fred Espen & Rüdiger, Barbara & Süss, Andre, 2018. "Ornstein–Uhlenbeck processes in Hilbert space with non-Gaussian stochastic volatility," Stochastic Processes and their Applications, Elsevier, vol. 128(2), pages 461-486.
    8. Kallsen, Jan & Muhle-Karbe, Johannes, 2010. "Exponentially affine martingales, affine measure changes and exponential moments of affine processes," Stochastic Processes and their Applications, Elsevier, vol. 120(2), pages 163-181, February.
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    Cited by:

    1. Martin Friesen & Sven Karbach, 2024. "Stationary covariance regime for affine stochastic covariance models in Hilbert spaces," Finance and Stochastics, Springer, vol. 28(4), pages 1077-1116, October.
    2. Benth, Fred Espen & Karbach, Sven, 2023. "Multivariate continuous-time autoregressive moving-average processes on cones," Stochastic Processes and their Applications, Elsevier, vol. 162(C), pages 299-337.
    3. Fred Espen Benth & Carlo Sgarra, 2024. "A Barndorff-Nielsen and Shephard model with leverage in Hilbert space for commodity forward markets," Finance and Stochastics, Springer, vol. 28(4), pages 1035-1076, October.
    4. Fred Espen Benth & Heidar Eyjolfsson, 2024. "Robustness of Hilbert space-valued stochastic volatility models," Finance and Stochastics, Springer, vol. 28(4), pages 1117-1146, October.
    5. Fred Espen Benth & Heidar Eyjolfsson, 2022. "Robustness of Hilbert space-valued stochastic volatility models," Papers 2211.16071, arXiv.org.

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