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Recursive Approaches for Multi-Layer Dividend Strategies in a Phase-Type Renewal Risk Model

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  • Apostolos D. Papaioannou

    (Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK
    These authors contributed equally to this work.)

  • Lewis Ramsden

    (School for Business and Society, University of York, York YO10 5DD, UK
    These authors contributed equally to this work.)

Abstract

In this paper we consider a risk model with two independent classes of insurance risks in the presence of a multi-layer dividend strategy. We assume that both of the claim number processes are renewal processes with phase-type inter-arrival times. By analysing the Markov chains associated with the two given phase-type distributions of the inter-arrival times, algorithmic schemes for the determination of explicit expressions for the Gerber–Shiu expected discounted penalty function, as well as the expected discounted dividend payments are derived, using two different approaches.

Suggested Citation

  • Apostolos D. Papaioannou & Lewis Ramsden, 2022. "Recursive Approaches for Multi-Layer Dividend Strategies in a Phase-Type Renewal Risk Model," Risks, MDPI, vol. 11(1), pages 1-21, December.
    • Handle: RePEc:gam:jrisks:v:11:y:2022:i:1:p:1-:d:1008541
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    References listed on IDEAS

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    1. Andrei Badescu & David Landriault, 2008. "Recursive Calculation of the Dividend Moments in a Multi-threshold Risk Model," North American Actuarial Journal, Taylor & Francis Journals, vol. 12(1), pages 74-88.
    2. Lin, X.Sheldon & Pavlova, Kristina P., 2006. "The compound Poisson risk model with a threshold dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 57-80, February.
    3. Andrei Badescu, 2008. "“The Discounted Joint Distribution of the Surplus Prior to Ruin and the Deficit at Ruin in a Sparre Andersen Model,” Jiandong Ren, July 2007," North American Actuarial Journal, Taylor & Francis Journals, vol. 12(2), pages 210-212.
    4. Lin, X. Sheldon & Sendova, Kristina P., 2008. "The compound Poisson risk model with multiple thresholds," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 617-627, April.
    5. Yang, Hu & Zhang, Zhimin, 2008. "Gerber-Shiu discounted penalty function in a Sparre Andersen model with multi-layer dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 984-991, June.
    6. Jing Xiao, 2007. "From the editor," Journal of Family and Economic Issues, Springer, vol. 28(1), pages 1-2, March.
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