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On the classical risk model with credit and debit interests under absolute ruin

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  • Wang, Chunwei
  • Yin, Chuancun
  • Li, Erqiang

Abstract

In this paper, we consider the dividend payments in a compound Poisson risk model with credit and debit interests under absolute ruin. We first obtain the integro-differential equations satisfied by the moment generating function and moments of the discounted aggregate dividend payments. Secondly, applying these results, we get the explicit expressions of them for exponential claims. Then, we give the numerical analysis of the optimal dividend barrier and the expected discounted aggregate dividend payments which are influenced by the debit and credit interests. Finally, we find the integro-differential equations satisfied by the Laplace transform of absolute ruin time and give its explicit expressions when the claim sizes are exponentially distributed.

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  • Wang, Chunwei & Yin, Chuancun & Li, Erqiang, 2010. "On the classical risk model with credit and debit interests under absolute ruin," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 427-436, March.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:5-6:p:427-436
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    References listed on IDEAS

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    1. Albrecher, Hansjorg & Claramunt, M.Merce & Marmol, Maite, 2005. "On the distribution of dividend payments in a Sparre Andersen model with generalized Erlang(n) interclaim times," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 324-334, October.
    2. Hans Gerber & Hailiang Yang, 2007. "Absolute Ruin Probabilities in a Jump Diffusion Risk Model with Investment," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(3), pages 159-169.
    3. Gerber, Hans U. & Shiu, Elias S.W. & Smith, Nathaniel, 2008. "Methods for estimating the optimal dividend barrier and the probability of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 243-254, February.
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    Cited by:

    1. Li, Shuanming & Lu, Yi, 2013. "On the generalized Gerber–Shiu function for surplus processes with interest," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 127-134.
    2. Li, Manman & Liu, Zaiming, 2012. "Regulated absolute ruin problem with interest structure and linear dividend barrier," Economic Modelling, Elsevier, vol. 29(5), pages 1786-1792.
    3. Yu, Wenguang, 2013. "Some results on absolute ruin in the perturbed insurance risk model with investment and debit interests," Economic Modelling, Elsevier, vol. 31(C), pages 625-634.
    4. Yunyun Wang & Wenguang Yu & Yujuan Huang & Xinliang Yu & Hongli Fan, 2019. "Estimating the Expected Discounted Penalty Function in a Compound Poisson Insurance Risk Model with Mixed Premium Income," Mathematics, MDPI, vol. 7(3), pages 1-25, March.

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