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Recursive Calculation of the Dividend Moments in a Multi-threshold Risk Model

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  • Andrei Badescu
  • David Landriault

Abstract

In this article, we consider the class of risk models with Markovian claim arrivals studied by Badescu et al. (2005) and Ramaswami (2006), among others. Under a multi-threshold dividend structure, we develop a recursive algorithm for the calculation of the moments of the discounted dividend payments before ruin. Capitalizing on the connection between an insurer’s surplus process and its corresponding fluid flow process, our approach generalizes results obtained by Albrecher and Hartinger (2007) and Zhou (2006) in the framework of the classical compound Poisson risk model (with phase-type claim sizes). Contrary to the traditional analysis of the discounted dividend payments in risk theory, we develop a sample-path-analysis procedure that allows the determination of these moments with or without ruin occurrence (separately). Numerical examples are then considered to illustrate our main results and show the contribution of each component to the moments of the discounted dividend payments.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:uaajxx:v:12:y:2008:i:1:p:74-88
    DOI: 10.1080/10920277.2008.10597501
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    Cited by:

    1. Olena Ragulina & Jonas Šiaulys, 2020. "Upper Bounds and Explicit Formulas for the Ruin Probability in the Risk Model with Stochastic Premiums and a Multi-Layer Dividend Strategy," Mathematics, MDPI, vol. 8(11), pages 1-35, October.
    2. Ahn, Soohan & Badescu, Andrei L. & Cheung, Eric C.K. & Kim, Jeong-Rae, 2018. "An IBNR–RBNS insurance risk model with marked Poisson arrivals," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 26-42.
    3. Cheung, Eric C.K. & Feng, Runhuan, 2013. "A unified analysis of claim costs up to ruin in a Markovian arrival risk model," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 98-109.
    4. Cheung, Eric C.K., 2013. "Moments of discounted aggregate claim costs until ruin in a Sparre Andersen risk model with general interclaim times," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 343-354.
    5. 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.

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