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

Jae-Kyung Woo () and Haibo Liu ()
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Jae-Kyung Woo: University of New South Wales
Haibo Liu: University of Iowa

Methodology and Computing in Applied Probability, 2018, vol. 20, issue 4, 1285-1318

Abstract: 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.

Keywords: Discounted aggregate claims until ruin; Discrete Sparre Andersen renewal risk process; Discounted moment-based joint distribution; Higher moments; Covariance; Discrete Coxian (K n) distribution; Claim causing ruin; 91B30; 60K10 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11009-018-9618-3

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