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Tempered infinitely divisible distributions and processes

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

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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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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  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, vol. 32(7), pages 1363-1378, July.
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