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The Tax Identity For Markov Additive Risk Processes

Author

Listed:
  • Hansjörg Albrecher

    (University of Lausanne
    Swiss Finance Institute)

  • Florin Avram

    (Université de Pau)

  • Corina Constantinescu

    (University of Lausanne
    University of Liverpool)

  • Jevgenijs Ivanovs

    (University of Lausanne)

Abstract

Taxed risk processes, i.e. processes which change their drift when reaching new maxima, represent a certain type of generalizations of Lévy and of Markov additive processes (MAP), since the times at which their Markovian mechanism changes are allowed to depend on the current position. In this paper we study generalizations of the tax identity of Albrecher and Hipp (2007) from the classical risk model to more general risk processes driven by spectrally-negative MAPs. We use the Sparre Andersen risk processes with phase-type interarrivals to illustrate the ideas in their simplest form.

Suggested Citation

  • Hansjörg Albrecher & Florin Avram & Corina Constantinescu & Jevgenijs Ivanovs, 2014. "The Tax Identity For Markov Additive Risk Processes," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 245-258, March.
    • Handle: RePEc:spr:metcap:v:16:y:2014:i:1:d:10.1007_s11009-012-9310-y
    DOI: 10.1007/s11009-012-9310-y
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    References listed on IDEAS

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    1. Jiandong Ren, 2007. "The Discounted Joint Distribution of the Surplus Prior to Ruin and the Deficit at Ruin in a Sparre Andersen Model," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(3), pages 128-136.
    2. Albrecher, Hansjörg & Borst, Sem & Boxma, Onno & Resing, Jacques, 2009. "The tax identity in risk theory -- a simple proof and an extension," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 304-306, April.
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    Citations

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    Cited by:

    1. Dalal Al Ghanim & Ronnie Loeffen & Alex Watson, 2018. "The equivalence of two tax processes," Papers 1811.01664, arXiv.org, revised Oct 2019.
    2. Avram, Florin & Vu, Nhat Linh & Zhou, Xiaowen, 2017. "On taxed spectrally negative Lévy processes with draw-down stopping," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 69-74.
    3. Wenyuan Wang & Zhimin Zhang, 2019. "Optimal loss-carry-forward taxation for L\'{e}vy risk processes stopped at general draw-down time," Papers 1904.08029, arXiv.org.
    4. Al Ghanim, Dalal & Loeffen, Ronnie & Watson, Alexander R., 2020. "The equivalence of two tax processes," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 1-6.
    5. Florin Avram & Danijel Grahovac & Ceren Vardar-Acar, 2019. "The W , Z / ν , δ Paradigm for the First Passage of Strong Markov Processes without Positive Jumps," Risks, MDPI, vol. 7(1), pages 1-15, February.

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