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Upper and lower bounds for the solutions of Markov renewal equations

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  • Gang Li
  • Jiaowan Luo

Abstract

Upper and lower bounds are studied for the solutions of Markov renewal equations. Some of their special cases are derived under specific marginal conditons and in an alternating environment. The method to construct the bounds is also explained in detail. At the end, these bounds are applied to a shock model and an age-dependent branching process under Markovian environment. Copyright Springer-Verlag 2005

Suggested Citation

  • Gang Li & Jiaowan Luo, 2005. "Upper and lower bounds for the solutions of Markov renewal equations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(2), pages 243-253, November.
    • Handle: RePEc:spr:mathme:v:62:y:2005:i:2:p:243-253
    DOI: 10.1007/s00186-005-0008-6
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    References listed on IDEAS

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    1. Asmussen, Søren & Henriksen, Lotte Fløe & Klüppelberg, Claudia, 1994. "Large claims approximations for risk processes in a Markovian environment," Stochastic Processes and their Applications, Elsevier, vol. 54(1), pages 29-43, November.
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    Cited by:

    1. 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.
    2. Li, Shu & Landriault, David & Lemieux, Christiane, 2015. "A risk model with varying premiums: Its risk management implications," Insurance: Mathematics and Economics, Elsevier, vol. 60(C), pages 38-46.

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    Keywords

    Markov renewal equation; Bounds;

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