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On the discrete-time compound renewal risk model with dependence

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  • Marceau, Etienne

Abstract

In this paper, we study the discrete-time renewal risk model with dependence between the claim amount random variable and the interclaim time random variable. We consider several dependence structures between the claim amount random variable and the interclaim time random variable. Recursive formulas are derived for the probability mass function and the moments of the total claim amount over a fixed period of time. In the context of ruin theory, explicit expressions for the expected penalty (Gerber-Shiu) function are derived for special cases. We also discuss how the discrete-time compound renewal risk model with dependence can be used to approximate the corresponding continuous time compound renewal risk model with dependence. Numerical examples are provided to illustrate different topics discussed in the paper.

Suggested Citation

  • Marceau, Etienne, 2009. "On the discrete-time compound renewal risk model with dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 245-259, April.
    • Handle: RePEc:eee:insuma:v:44:y:2009:i:2:p:245-259
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    Cited by:

    1. He Liu & Zhenhua Bao, 2015. "On a Discrete Interaction Risk Model with Delayed Claims," JRFM, MDPI, vol. 8(4), pages 1-14, September.
    2. Jae-Kyung Woo & Haibo Liu, 2018. "Discounted Aggregate Claim Costs Until Ruin in the Discrete-Time Renewal Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1285-1318, December.
    3. Cossette, Hélène & Marceau, Etienne & Perreault, Samuel, 2015. "On two families of bivariate distributions with exponential marginals: Aggregation and capital allocation," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 214-224.

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