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Tempered infinitely divisible distributions and processes

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  • Bianchi, Michele Leonardo
  • Rachev, Svetlozar T.
  • Kim, Young Shin
  • Fabozzi, Frank J.

Abstract

In this paper, we construct the new class of tempered infinitely divisible (TID) distributions. Taking into account the tempered stable distribution class, as introduced by in the seminal work of Rosinsky , a modification of the tempering function allows one to obtain suitable properties. In particular, TID distributions may have exponential moments of any order and conserve all proper properties of the Rosinski setting. Furthermore, we prove that the modified tempered stable distribution is TID and give some further parametric example. --

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Bibliographic Info

Paper provided by Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering in its series Working Paper Series in Economics with number 26.

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Date of creation: 2011
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Handle: RePEc:zbw:kitwps:26

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Web page: http://www.wiwi.kit.edu/
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Related research

Keywords: stable distributions; tempered stable distributions; tempered infinitely divisible distributions; modified tempered stable distributions;

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  1. Kim, Young Shin & Rachev, Svetlozar T. & Bianchi, Michele Leonardo & Fabozzi, Frank J., 2008. "Financial market models with Lévy processes and time-varying volatility," Journal of Banking & Finance, Elsevier, Elsevier, vol. 32(7), pages 1363-1378, July.
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Cited by:
  1. Young Shin Kim & Rachev, Svetlozar T. & Bianchi, Michele Leonardo & Mitov, Ivan & Fabozzi, Frank J., 2010. "Time series analysis for financial market meltdowns," Working Paper Series in Economics 2, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
  2. Schosser, Stephan & Vogt, Bodo, 2011. "The public loss game: An experimental study of public bads," Working Paper Series in Economics 33, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
  3. Schaffer, Axel, 2011. "Appropriate policy measures to attract private capital in consideration of regional efficiency in using infrastructure and human capital," Working Paper Series in Economics 31, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
  4. Küchler, Uwe & Tappe, Stefan, 2013. "Tempered stable distributions and processes," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 123(12), pages 4256-4293.
  5. Küchler, Uwe & Tappe, Stefan, 2014. "Exponential stock models driven by tempered stable processes," Journal of Econometrics, Elsevier, Elsevier, vol. 181(1), pages 53-63.

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