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Affine processes on positive semidefinite matrices

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  • Christa Cuchiero
  • Damir Filipovi\'c
  • Eberhard Mayerhofer
  • Josef Teichmann
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    Abstract

    This article provides the mathematical foundation for stochastically continuous affine processes on the cone of positive semidefinite symmetric matrices. This analysis has been motivated by a large and growing use of matrix-valued affine processes in finance, including multi-asset option pricing with stochastic volatility and correlation structures, and fixed-income models with stochastically correlated risk factors and default intensities.

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    File URL: http://arxiv.org/pdf/0910.0137
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 0910.0137.

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    Date of creation: Oct 2009
    Date of revision: Apr 2011
    Publication status: Published in Annals of Applied Probability 2011, Vol. 21, No. 2, 397-463
    Handle: RePEc:arx:papers:0910.0137

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    Web page: http://arxiv.org/

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    1. Bru, Marie-France, 1989. "Diffusions of perturbed principal component analysis," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 29(1), pages 127-136, April.
    2. José Fonseca & Martino Grasselli & Claudio Tebaldi, 2007. "Option pricing when correlations are stochastic: an analytical framework," Review of Derivatives Research, Springer, Springer, vol. 10(2), pages 151-180, May.
    3. JosE Da Fonseca & Martino Grasselli & Claudio Tebaldi, 2008. "A multifactor volatility Heston model," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 8(6), pages 591-604.
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    Cited by:
    1. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2014. "A general HJM framework for multiple yield curve modeling," Papers 1406.4301, arXiv.org.
    2. Jos\'e Da Fonseca & Alessandro Gnoatto & Martino Grasselli, 2012. "A flexible matrix Libor model with smiles," Papers 1203.4786, arXiv.org.
    3. Ahdida, Abdelkoddousse & Alfonsi, Aurélien, 2013. "A mean-reverting SDE on correlation matrices," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 123(4), pages 1472-1520.
    4. Christa Cuchiero & Josef Teichmann, 2011. "Path properties and regularity of affine processes on general state spaces," Papers 1107.1607, arXiv.org, revised Jan 2013.
    5. Kang, Chulmin & Kang, Wanmo, 2013. "Transform formulae for linear functionals of affine processes and their bridges on positive semidefinite matrices," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 123(6), pages 2419-2445.
    6. Mayerhofer, Eberhard, 2012. "Affine processes on positive semidefinite d×d matrices have jumps of finite variation in dimension d>1," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 122(10), pages 3445-3459.
    7. Mayerhofer, Eberhard & Pfaffel, Oliver & Stelzer, Robert, 2011. "On strong solutions for positive definite jump diffusions," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 121(9), pages 2072-2086, September.
    8. Archil Gulisashvili & Josef Teichmann, 2014. "The G\"{a}rtner-Ellis theorem, homogenization, and affine processes," Papers 1406.3716, arXiv.org.
    9. Antonis Papapantoleon, 2011. "Computation of copulas by Fourier methods," Papers 1108.1216, arXiv.org, revised Jun 2014.

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