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Discounted Aggregate Claim Costs Until Ruin in the Discrete-Time Renewal Risk Model

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Abstract

In this paper, we focus on analyzing the relationship between the discounted aggregate claim costs until ruin and ruin-related quantities including the time of ruin. To facilitate the evaluation of quantities of our interest as an approximation to the ones in the continuous case, discrete-time renewal risk model with certain dependent structure between interclaim times and claim amounts is considered. Furthermore, to provide explicit expressions for various moment-based joint probabilities, a fairly general class of distributions, namely the discrete Coxian distribution, is used for the interclaim times. Also, we assume a combination of geometrics claim size with arbitrary interlciam time distribution to derive a nice expression for the Gerber-Shiu type function involving the discounted aggregate claims until ruin. Consequently, the results are applied to evaluate some interesting quantities including the covariance between the discounted aggregate claim costs until ruin and the discounted claim causing ruin given that ruin occurs.

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Acknowledgements

The authors are grateful to the anonymous referees and the Editor for their useful suggestions that have greatly improved the overall presentation and material of the paper.

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Authors and Affiliations

  1. School of Risk and Actuarial Studies, Australian School of Business, University of New South Wales, Sydney, Australia

    Jae-Kyung Woo

  2. Department of Statistics and Actuarial Science, University of Iowa, Iowa City, IA, USA

    Haibo Liu

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  1. Jae-Kyung Woo
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  2. Haibo Liu
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Correspondence to Jae-Kyung Woo.

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Woo, JK., Liu, H. Discounted Aggregate Claim Costs Until Ruin in the Discrete-Time Renewal Risk Model. Methodol Comput Appl Probab 20, 1285–1318 (2018). https://doi.org/10.1007/s11009-018-9618-3

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  • DOI: https://doi.org/10.1007/s11009-018-9618-3

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