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Some results on absolute ruin in the perturbed insurance risk model with investment and debit interests

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  • Yu, Wenguang

Abstract

In this paper, we consider a perturbed compound Poisson risk model with investment and debit interests. Dividends are paid to the shareholders according to a threshold dividend strategy. An alternative assumption is that when the surplus is negative, a debit interest is applied and when the surplus is above a certain positive level, the insurer could earn investment interest. Integro-differential equations with boundary conditions satisfied by the moment-generating function, the nth moment of the present value of all dividends until absolute ruin and the Gerber–Shiu expected discounted penalty function are obtained. Then, we present the explicit expressions for the zero discounted nth moment of the present value of all dividends until absolute ruin in the case of exponential claims. Finally, numerical example is also given to illustrate the effect of the related parameters on the first moment of the present value of all dividends until absolute ruin.

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  • 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.
    • Handle: RePEc:eee:ecmode:v:31:y:2013:i:c:p:625-634
    DOI: 10.1016/j.econmod.2012.12.020
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    References listed on IDEAS

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    1. 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.
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    Cited by:

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    2. Aparna B. S & Neelesh S Upadhye, 2019. "On the Compound Beta-Binomial Risk Model with Delayed Claims and Randomized Dividends," Papers 1908.03407, arXiv.org.
    3. 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.
    4. Wen Su & Wenguang Yu, 2020. "Asymptotically Normal Estimators of the Gerber-Shiu Function in Classical Insurance Risk Model," Mathematics, MDPI, vol. 8(10), pages 1-11, September.
    5. Jiechang Ruan & Wenguang Yu & Ke Song & Yihan Sun & Yujuan Huang & Xinliang Yu, 2019. "A Note on a Generalized Gerber–Shiu Discounted Penalty Function for a Compound Poisson Risk Model," Mathematics, MDPI, vol. 7(10), pages 1-12, September.

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