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Kac–Lévy Processes

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  • Nikita Ratanov

    (Universidad del Rosario)

Abstract

Markov-modulated Lévy processes with two different regimes of restarting are studied. These regimes correspond to the completely renewed process and to the process of Markov modulation, accompanied by jumps. We give explicit expressions for the Lévy–Khintchine exponent in the case of a two-state underlying Markov chain. For the renewal case, the limit distributions (as $$t\rightarrow \infty $$t→∞) are obtained. In the case of processes with jumps, we present some results for the exponential functional.

Suggested Citation

  • Nikita Ratanov, 2020. "Kac–Lévy Processes," Journal of Theoretical Probability, Springer, vol. 33(1), pages 239-267, March.
    • Handle: RePEc:spr:jotpro:v:33:y:2020:i:1:d:10.1007_s10959-018-0873-6
    DOI: 10.1007/s10959-018-0873-6
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    References listed on IDEAS

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    1. Robert J. Elliott & Leunglung Chan & Tak Kuen Siu, 2005. "Option pricing and Esscher transform under regime switching," Annals of Finance, Springer, vol. 1(4), pages 423-432, October.
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    6. Chevallier Julien & Goutte Stéphane, 2017. "On the estimation of regime-switching Lévy models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(1), pages 3-29, February.
    7. Thomas W Epps, 2007. "Pricing Derivative Securities," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6243, February.
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