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On a generalization of the expected discounted penalty function in a discrete‐time insurance risk model

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  • David Landriault

Abstract

In this paper, we propose a generalization of the expected discounted penalty function and analyze the proposed analytic tool in the framework of the compound binomial model with a general premium rate c (c ∈ ℕ+) received per period. We derive an explicit expression for this generalized analytic tool in terms of the zeros of a matrix determinant. We then examine the original expected discounted penalty function in the compound binomial model with a general premium rate c, generalizing the results of Cheng et al. (Insur. Math. Econ. 2000; 26:239–250) in the framework of the compound binomial model with a unit premium rate. A numerical example is then considered to compare the original expected discounted penalty function with its generalized analytic tool. Copyright © 2008 John Wiley & Sons, Ltd.

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  • David Landriault, 2008. "On a generalization of the expected discounted penalty function in a discrete‐time insurance risk model," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(6), pages 525-539, November.
    • Handle: RePEc:wly:apsmbi:v:24:y:2008:i:6:p:525-539
    DOI: 10.1002/asmb.713
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    References listed on IDEAS

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    Cited by:

    1. He, Yue & Kawai, Reiichiro & Shimizu, Yasutaka & Yamazaki, Kazutoshi, 2023. "The Gerber-Shiu discounted penalty function: A review from practical perspectives," Insurance: Mathematics and Economics, Elsevier, vol. 109(C), pages 1-28.
    2. Xie, Jie-hua & Zou, Wei, 2010. "Expected present value of total dividends in a delayed claims risk model under stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 415-422, April.
    3. Yue He & Reiichiro Kawai & Yasutaka Shimizu & Kazutoshi Yamazaki, 2022. "The Gerber-Shiu discounted penalty function: A review from practical perspectives," Papers 2203.10680, arXiv.org, revised Dec 2022.

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