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Time-inhomogeneous polynomial processes

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  • Mar'ia Fernanda del Carmen Agoitia Hurtado
  • Thorsten Schmidt

Abstract

Time homogeneous polynomial processes are Markov processes whose moments can be calculated easily through matrix exponentials. In this work, we develop a notion of time inhomogeneous polynomial processes where the coeffiecients of the process may depend on time. A full characterization of this model class is given by means of their semimartingale characteristics. We show that in general, the computation of moments by matrix exponentials is no longer possible. As an alternative we explore a connection to Magnus series for fast numerical approximations. Time-inhomogeneity is important in a number of applications: in term-structure models, this allows a perfect calibration to available prices. In electricity markets, seasonality comes naturally into play and have to be captured by the used models. The model class studied in this work extends existing models, for example Sato processes and time-inhomogeneous affine processes.

Suggested Citation

  • Mar'ia Fernanda del Carmen Agoitia Hurtado & Thorsten Schmidt, 2018. "Time-inhomogeneous polynomial processes," Papers 1806.03887, arXiv.org.
    • Handle: RePEc:arx:papers:1806.03887
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    References listed on IDEAS

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    1. Martin Keller-Ressel & Thorsten Schmidt & Robert Wardenga, 2018. "Affine processes beyond stochastic continuity," Papers 1804.07556, arXiv.org, revised Dec 2018.
    2. Julie Lyng Forman & Michael Sørensen, 2008. "The Pearson Diffusions: A Class of Statistically Tractable Diffusion Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 438-465, September.
    3. Christa Cuchiero & Martin Keller-Ressel & Josef Teichmann, 2012. "Polynomial processes and their applications to mathematical finance," Finance and Stochastics, Springer, vol. 16(4), pages 711-740, October.
    4. Gourieroux, Christian & Jasiak, Joann, 2006. "Multivariate Jacobi process with application to smooth transitions," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 475-505.
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