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On the distribution of exponential functionals for Lévy processes with jumps of rational transform

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  • Kuznetsov, A.

Abstract

We derive explicit formulas for the Mellin transform and the distribution of the exponential functional for Lévy processes with rational Laplace exponent. This extends recent results by Cai and Kou [3] on the processes with hyper-exponential jumps.

Suggested Citation

  • Kuznetsov, A., 2012. "On the distribution of exponential functionals for Lévy processes with jumps of rational transform," Stochastic Processes and their Applications, Elsevier, vol. 122(2), pages 654-663.
    • Handle: RePEc:eee:spapps:v:122:y:2012:i:2:p:654-663
    DOI: 10.1016/j.spa.2011.09.007
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    References listed on IDEAS

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    1. Sonia Fourati, 2010. "Explicit solutions for the exit problem for a class of L\'evy processes. Applications to the pricing of double barrier options," Papers 1003.4917, arXiv.org.
    2. Maulik, Krishanu & Zwart, Bert, 2006. "Tail asymptotics for exponential functionals of Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 116(2), pages 156-177, February.
    3. Chaumont, L. & Kyprianou, A.E. & Pardo, J.C., 2009. "Some explicit identities associated with positive self-similar Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 119(3), pages 980-1000, March.
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    Citations

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    Cited by:

    1. D. Hackmann & A. Kuznetsov, 2014. "Asian options and meromorphic Lévy processes," Finance and Stochastics, Springer, vol. 18(4), pages 825-844, October.
    2. Runhuan Feng & Alexey Kuznetsov & Fenghao Yang, 2016. "Exponential functionals of Levy processes and variable annuity guaranteed benefits," Papers 1610.00577, arXiv.org.
    3. Nikita Ratanov, 2020. "Kac–Lévy Processes," Journal of Theoretical Probability, Springer, vol. 33(1), pages 239-267, March.
    4. Feng, Runhuan & Kuznetsov, Alexey & Yang, Fenghao, 2019. "Exponential functionals of Lévy processes and variable annuity guaranteed benefits," Stochastic Processes and their Applications, Elsevier, vol. 129(2), pages 604-625.
    5. Lan Wu & Jiang Zhou & Shuang Yu, 2017. "Occupation Times of General Lévy Processes," Journal of Theoretical Probability, Springer, vol. 30(4), pages 1565-1604, December.

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