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A Note on Wiener–Hopf Factorization for Markov Additive Processes

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  • Przemysław Klusik

    (University of Wrocław)

  • Zbigniew Palmowski

    (University of Wrocław)

Abstract

We prove the Wiener–Hopf factorization for Markov additive processes. We derive also Spitzer–Rogozin theorem for this class of processes which serves for obtaining Kendall’s formula and Fristedt representation of the cumulant matrix of the ladder epoch process. Finally, we also obtain the so-called ballot theorem.

Suggested Citation

  • Przemysław Klusik & Zbigniew Palmowski, 2014. "A Note on Wiener–Hopf Factorization for Markov Additive Processes," Journal of Theoretical Probability, Springer, vol. 27(1), pages 202-219, March.
    • Handle: RePEc:spr:jotpro:v:27:y:2014:i:1:d:10.1007_s10959-012-0425-4
    DOI: 10.1007/s10959-012-0425-4
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    References listed on IDEAS

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    1. A. B. Dieker & M. Mandjes, 2011. "Extremes of Markov-additive Processes with One-sided Jumps, with Queueing Applications," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 221-267, June.
    2. D'Auria, Bernardo & Kella, Offer & Ivanovs, Jevgenijs & Mandjes, Michel, 2010. "First passage of a Markov additive process and generalized Jordan chains," DES - Working Papers. Statistics and Econometrics. WS ws103923, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. Asmussen, Søren & Avram, Florin & Pistorius, Martijn R., 2004. "Russian and American put options under exponential phase-type Lévy models," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 79-111, January.
    4. Fourati, Sonia, 2012. "Explicit solutions of the exit problem for a class of Lévy processes; applications to the pricing of double-barrier options," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 1034-1067.
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    Keywords

    Levy process; Wiener–Hopf factorization;

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