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On Distributions of Runs in the Compound Binomial Risk Model

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  • Serkan Eryilmaz

    (Atilim University)

Abstract

This paper is concerned with the distribution of runs associated with claim indicators in a compound binomial risk model. We study the total number of claims, the longest run without claim, the shortest run without claim and the total number of runs up to a fixed period before the occurrence of a ruin. These quantities are potentially useful for an investment strategy of an insurance company and for understanding the behavior of a specific portfolio over time. We obtain recursive equations for the exact distributions of these random variables. We also illustrate the theoretical results with numerical computations.

Suggested Citation

  • Serkan Eryilmaz, 2014. "On Distributions of Runs in the Compound Binomial Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 149-159, March.
    • Handle: RePEc:spr:metcap:v:16:y:2014:i:1:d:10.1007_s11009-012-9303-x
    DOI: 10.1007/s11009-012-9303-x
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    References listed on IDEAS

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    1. José Luis Palacios, 2010. "Runs of Markov Chains and Streaks in Baseball," Methodology and Computing in Applied Probability, Springer, vol. 12(4), pages 659-665, December.
    2. Claude Lefèvre & Stéphane Loisel, 2008. "On Finite-Time Ruin Probabilities for Classical Risk Models," Post-Print hal-00168958, HAL.
    3. Willmot, Gordon E., 1993. "Ruin probabilities in the compound binomial model," Insurance: Mathematics and Economics, Elsevier, vol. 12(2), pages 133-142, April.
    4. Gerber, Hans U., 1988. "Mathematical Fun with the Compound Binomial Process," ASTIN Bulletin, Cambridge University Press, vol. 18(2), pages 161-168, November.
    5. EryIlmaz, Serkan, 2011. "Joint distribution of run statistics in partially exchangeable processes," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 163-168, January.
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    Cited by:

    1. Aparna B. S & Neelesh S Upadhye, 2019. "On the Compound Beta-Binomial Risk Model with Delayed Claims and Randomized Dividends," Papers 1908.03407, arXiv.org.
    2. Makri, Frosso S. & Psillakis, Zaharias M. & Arapis, Anastasios N., 2015. "Length of the minimum sequence containing repeats of success runs," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 28-37.

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