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Hypo-exponential distributions and compound Poisson processes with alternating parameters

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  • Ratanov, Nikita

Abstract

Point processes with alternating arrival rates arise in various applications, including financial modelling. We obtain explicit expressions for the distributions of these processes, i.e. for the sums ∑m=1nX(m) and ∑m=1n(−1)mX(m), where X(m) are independent exponentially distributed random variables with alternating parameters.

Suggested Citation

  • Ratanov, Nikita, 2015. "Hypo-exponential distributions and compound Poisson processes with alternating parameters," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 71-78.
    • Handle: RePEc:eee:stapro:v:107:y:2015:i:c:p:71-78
    DOI: 10.1016/j.spl.2015.08.006
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    References listed on IDEAS

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    1. Antonio Di Crescenzo & Shelemyahu Zacks, 2015. "Probability Law and Flow Function of Brownian Motion Driven by a Generalized Telegraph Process," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 761-780, September.
    2. Nikita Ratanov, 2007. "A jump telegraph model for option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 575-583.
    3. Nikita Ratanov, 2008. "Option Pricing Model Based on a Markov-modulated Diffusion with Jumps," Papers 0812.0761, arXiv.org.
    4. Nikita Ratanov, 2015. "Telegraph Processes with Random Jumps and Complete Market Models," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 677-695, September.
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    Cited by:

    1. Kim-Hung Li & Cheuk Ting Li, 2019. "Linear Combination of Independent Exponential Random Variables," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 253-277, March.

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